Explain why the square root of a number is defined to be equal to that number to the 1/2 power.

This is essentially a rule in the unit of radicals, where n✔️X^m = X^m/n. If the value of m is equal to n, as in 2✔️3^2 it would simply be 3^2/2 which is nothing but 3^1 = 3. Basically, the m value can be greater than n and or less than n, but if it is equal the m and n values cancel out.

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MrRoyal MrRoyal · Answer 2 · 2021-11-02T14:25:19+01:00

The square root of a number is a number, when multiplied by itself, equals a desired value.

See below for proof

The square root of a number n, is represented as:

[tex]\mathbf{\sqrt{n}}[/tex]

This can be rewritten as:

[tex]\mathbf{\sqrt{n} = \sqrt[2]{n}}[/tex]

According to law of indices

[tex]\mathbf{\sqrt[x]{m} = x^\frac{1}{m}}[/tex]

Using the above rule, we have:

[tex]\mathbf{\sqrt{n} = n^\frac{1}{2}}[/tex]

Hence, the square root of a number is the same as the number to the power of 1/2