Maths-
General
Easy

Question

Rationalize the denominator:fraction numerator 1 over denominator square root of 3 plus square root of 2 minus 1 end fraction

hintHint:

Hint:
Rationalization is a technique which is used to eliminate the irrational number in the denominator. For example, fraction numerator 1 over denominator square root of 2 end fraction
can be rationalised as fraction numerator 1 over denominator square root of 3 end fraction cross times fraction numerator square root of 3 over denominator square root of 3 end fraction equals fraction numerator square root of 3 over denominator 3 end fraction

The correct answer is: SQRT6-2+SQRT2/4


    Let’s say x equals fraction numerator 1 over denominator square root of 3 plus square root of 2 minus 1 end fraction
    As in the denominator, there are two irrational numbers i.e  square root of 2and square root of 3 , so first we will multiply and divide square root of 3 minus left parenthesis square root of 2 minus 1 right parenthesis
    table attributes columnalign right left right left right left right left right left right left columnspacing 0em 2em 0em 2em 0em 2em 0em 2em 0em 2em 0em end attributes row cell x equals fraction numerator 1 over denominator square root of 3 plus left parenthesis square root of 2 minus 1 right parenthesis end fraction cross times fraction numerator square root of 3 minus left parenthesis square root of 2 minus 1 right parenthesis over denominator square root of 3 minus left parenthesis square root of 2 minus 1 right parenthesis end fraction end cell row cell equals fraction numerator square root of 3 minus left parenthesis square root of 2 minus 1 right parenthesis over denominator 3 minus left parenthesis square root of 2 minus 1 right parenthesis squared end fraction end cell row cell equals fraction numerator square root of 3 minus square root of 2 plus 1 over denominator 3 minus left parenthesis 2 plus 1 minus 2 square root of 2 right parenthesis end fraction end cell row cell equals fraction numerator square root of 3 minus square root of 2 plus 1 over denominator 3 minus 3 plus 2 square root of 2 end fraction end cell row cell equals fraction numerator square root of 3 minus square root of 2 plus 1 over denominator 2 square root of 2 end fraction cross times fraction numerator square root of 2 over denominator square root of 2 end fraction end cell row cell equals fraction numerator square root of 6 minus 2 plus square root of 2 over denominator blank end fraction end cell end table
    Final Answer:
    Hence, after rationalizing the denominator, we get .fraction numerator square root of 6 minus 2 plus square root of 2 over denominator 4 end fraction

    Related Questions to study

    General
    Maths-

    Simplify  fraction numerator 1 plus square root of 2 over denominator square root of 5 plus square root of 3 end fraction plus fraction numerator 1 minus square root of 2 over denominator square root of 5 minus square root of 3 end fraction

    Simplify  fraction numerator 1 plus square root of 2 over denominator square root of 5 plus square root of 3 end fraction plus fraction numerator 1 minus square root of 2 over denominator square root of 5 minus square root of 3 end fraction

    Maths-General
    General
    Maths-

    Nina, Shanti and Belle run a 1000 m race at a constant speed. When Nina crossed the finish line first, she was 200 m ahead of Shanti and 400 m ahead of Belle. When Shanti crossed the finish line, how far ahead of Belle was she?

    Nina, Shanti and Belle run a 1000 m race at a constant speed. When Nina crossed the finish line first, she was 200 m ahead of Shanti and 400 m ahead of Belle. When Shanti crossed the finish line, how far ahead of Belle was she?

    Maths-General
    General
    Maths-

    The wheels on Charlie’s bike have a circumference of 1.5 m. When Charlie is riding fastest, the wheels rotate at a speed of five turns per second. a) What is the fastest speed Charlie can ride his bike, in km/h? b) How far would Charlie travel in 5 minutes at his fastest speed?

    The wheels on Charlie’s bike have a circumference of 1.5 m. When Charlie is riding fastest, the wheels rotate at a speed of five turns per second. a) What is the fastest speed Charlie can ride his bike, in km/h? b) How far would Charlie travel in 5 minutes at his fastest speed?

    Maths-General
    parallel
    General
    Maths-

    Walter and William have a height ratio of 7:8. If William has a height of 152 cm, how tall is Walter?

    Walter and William have a height ratio of 7:8. If William has a height of 152 cm, how tall is Walter?

    Maths-General
    General
    Maths-

    A saltwater swimming pool requires 2 kg of salt to be added for every 10000 litres of water. Joan’s swimming pool is 1.5 metres deep, 5 metres wide and 15 metres long. How much salt will she need to add to her pool?

    A saltwater swimming pool requires 2 kg of salt to be added for every 10000 litres of water. Joan’s swimming pool is 1.5 metres deep, 5 metres wide and 15 metres long. How much salt will she need to add to her pool?

    Maths-General
    General
    Maths-

    The Bionic Woman gives Batman a 12 second start in a 2 kilometre race. If the Bionic Woman runs at 5 km/min, and Batman runs at 3 km/min, who will win the race and by how many seconds

    The Bionic Woman gives Batman a 12 second start in a 2 kilometre race. If the Bionic Woman runs at 5 km/min, and Batman runs at 3 km/min, who will win the race and by how many seconds

    Maths-General
    parallel
    General
    Maths-

    At a school camp there is enough food for 150 students for 5 days. a) How long would the food last if there were only 100 students? b) If the food ran out after only 4 days, how many students attended the camp?

    At a school camp there is enough food for 150 students for 5 days. a) How long would the food last if there were only 100 students? b) If the food ran out after only 4 days, how many students attended the camp?

    Maths-General
    General
    Maths-

    Michelle can complete a landscaping job in 6 days and Danielle can complete the same job in 4 days. Working together, in how many days could they complete the job?

    Michelle can complete a landscaping job in 6 days and Danielle can complete the same job in 4 days. Working together, in how many days could they complete the job?

    Maths-General
    General
    Maths-

    The required staff to student ratio for an excursion is 2 : 15. If 10 teachers attend the excursion, what is the maximum number of students who can attend?

    The required staff to student ratio for an excursion is 2 : 15. If 10 teachers attend the excursion, what is the maximum number of students who can attend?

    Maths-General
    parallel
    General
    Maths-

    Julie and Jeanette enjoy finishing their 6 km morning run together. Julie runs at an average speed of 10 km/h and Jeanette runs at an average speed of 3 m/s. If Julie leaves at 8 a.m., at what time should Jeanette leave if they are to finish their run at the same time?

    Julie and Jeanette enjoy finishing their 6 km morning run together. Julie runs at an average speed of 10 km/h and Jeanette runs at an average speed of 3 m/s. If Julie leaves at 8 a.m., at what time should Jeanette leave if they are to finish their run at the same time?

    Maths-General
    General
    Maths-

    Find the values of a and b : fraction numerator 5 plus 3 square root of 2 over denominator 5 minus 3 square root of 2 end fraction equals a plus b square root of 2

    Find the values of a and b : fraction numerator 5 plus 3 square root of 2 over denominator 5 minus 3 square root of 2 end fraction equals a plus b square root of 2

    Maths-General
    General
    Maths-

    if fraction numerator 4 plus square root of 5 over denominator 4 minus square root of 5 end fraction plus fraction numerator 4 minus square root of 5 over denominator 4 plus square root of 5 end fraction equals a plus b square root of 5. Then, find the values of a and b.

    if fraction numerator 4 plus square root of 5 over denominator 4 minus square root of 5 end fraction plus fraction numerator 4 minus square root of 5 over denominator 4 plus square root of 5 end fraction equals a plus b square root of 5. Then, find the values of a and b.

    Maths-General
    parallel
    General
    Maths-

    A rainfall of 0.896 cm was recorded in 7 hours. What was the average amount of rainfall per hour?

    A rainfall of 0.896 cm was recorded in 7 hours. What was the average amount of rainfall per hour?

    Maths-General
    General
    Maths-

    Three bricklayers, Maric, Hugh and Ethan, are cladding a new home. If Maric were to work alone, the job would take him 8 days to complete. If Hugh were to work alone, the job would take him 6 days to complete and if Ethan were to work by himself, the job would take him 12 days to complete. a) If the three men work together, how long will it take them to complete the job? b) What fraction of the house will each bricklayer complete?

    Three bricklayers, Maric, Hugh and Ethan, are cladding a new home. If Maric were to work alone, the job would take him 8 days to complete. If Hugh were to work alone, the job would take him 6 days to complete and if Ethan were to work by himself, the job would take him 12 days to complete. a) If the three men work together, how long will it take them to complete the job? b) What fraction of the house will each bricklayer complete?

    Maths-General
    General
    Maths-

    A can do a piece of work in 40 days and B in 45 days. They work together for 10 days and then B goes away. In how many days will A finish the remaining work?

    A can do a piece of work in 40 days and B in 45 days. They work together for 10 days and then B goes away. In how many days will A finish the remaining work?

    Maths-General
    parallel

    card img

    With Turito Academy.

    card img

    With Turito Foundation.

    card img

    Get an Expert Advice From Turito.

    Turito Academy

    card img

    With Turito Academy.

    Test Prep

    card img

    With Turito Foundation.