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Maths-

General

Easy

Question

Simplify 4√12+5√27 - 3√75 +√300

hint Hint:

Use prime factorization.

The correct answer is: 18√3

Complete step by step solution:
On prime factorization, we can write
$4 square root of 12 equals 4 cross times square root of 2 cross times 2 cross times 3 end root comma 5 square root of 27 equals 5 cross times square root of 3 cross times 3 cross times 3 end root comma 3 square root of 75 equals 3 cross times square root of 3 cross times 5 cross times 5 end root$
and $square root of 300 equals square root of 2 cross times 2 cross times 3 cross times 5 cross times 5 end root$
This can be written as $8 square root of 3 comma 15 square root of 3 comma 15 square root of 3$ and $10 square root of 3$ respectively.
So, $4 square root of 12 plus 5 square root of 27 minus 3 square root of 75 plus square root of 300 equals 8 square root of 3 plus 15 square root of 3 minus 15 square root of 3 plus 10 square root of 3 equals 18 square root of 3$

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