A 'quareroot' (which is commonly known as a fourth root) of a number is a value that, when raised to the power of 4, gives the original number. In terms of indices, it is written as x^(1/4) or √[4]x. Let's use an example to illustrate: Find the fourth root of 16. Step 1: Express the fourth root using index notation. √[4]16 = 16^(1/4) Step 2: Find a number that, when multiplied by itself four times, equals 16. We know that 2 × 2 × 2 × 2 = 16. Step 3: State the result. Therefore, 16^(1/4) = 2.

Using quareroot

July 9, 2026Mathematics

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Answer

16^{\frac{1}{4}} = 2

Step-by-step solution

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A 'quareroot' (which is commonly known as a fourth root) of a number is a value that, when raised to the power of 4, gives the original number. In terms of indices, it is written as $x^{\frac{1}{4}}$ or $\sqrt[4]{x}$ .

Let's use an example to illustrate: Find the fourth root of 16.

Express the fourth root using index notation.
$\sqrt[4]{16} = 16^{\frac{1}{4}}$
Find a number that, when multiplied by itself four times, equals 16.
We know that $2 \times 2 \times 2 \times 2 = 16$ .
State the result.
Therefore, $16^{\frac{1}{4}} = \boxed{2}$ .

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