Question

What is the square root of show your workings

√ 81 / 625​

Answer 1

81 = 3⁴

√81

= √3⁴

=√(3²)(3²)

=√(3²)²

=3²

=3x3

=9

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√625

=√5⁴

=√(5²)(5²)

=√(5²)²

=5x5

=25

Answer 2

The sqrt function has the distributive property.

So sqrt(a/b) = sqrt(a) / sqrt(b).

In this case, a = 81, and b = 625.

sqrt(81) = 9.

sqrt(625) = 25.

So sqrt(81/625) = 9 / 25.

To get a decimal representation, multiply by a form of 1 that makes the denominator a power of 10. Here, 25 * 4 = 100, so

9/25 * 4/4 = 36/100 = 0.36