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Maths-

General

Easy

Question

Convert $fourth root of 3$ and $root index 6 of 2$ into surds of the same order.

hint Hint:

Hint:
Surds are the square roots of numbers that cannot be simplified into a whole or rational number and they cannot be represented in a fraction. The order of a surd indicates the index of root to be extracted. For example in $n-th root of a$ , n is called the order of the surd.

The correct answer is: 000

We need to convert $fourth root of 3$ and $root index 6 of 2$ into surds of the same order. $fourth root of 3 text and end text root index 6 of 2$ can be written as $3 to the power of 1 fourth end exponent$
and $2 to the power of 1 over 6 end exponent$
$3 to the power of 1 fourth end exponent$ can be written as
$3 to the power of 1 fourth end exponent equals 3 to the power of 3 over 12 end exponent equals open parentheses 3 cubed close parentheses to the power of 1 over 12 end exponent equals 27 1 over 12 equals root index 12 of 27$
$2 to the power of 1 over 6 end exponent$ can be written as
$2 to the power of 1 over 6 end exponent equals 2 to the power of 2 over 12 end exponent equals open parentheses 2 squared close parentheses to the power of 1 over 12 end exponent equals 4 to the power of 1 over 12 end exponent equals root index 12 of 4$
So, when $fourth root of 3$ and $root index 6 of 2$ is converted to surds with the same order, they will have an order of 12.
Final Answer:
Hence, $root index 12 of 27 text and end text root index 12 of 4$ are the same order surds of $fourth root of 3 text and end text root index space 6 of 2$

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