Question

What is the square root of 108 in simplified radical form?

Answer 1

heya..

Let's take √(108) through these steps. First, we rewrite 108 as a product of a perfect square and another number. Notice that 108 is divisible by 4, and 4 is a perfect square, so we can rewrite 108 as 4 × 27.

√(108) = √(4 × 27)

Now, write the square root as a product of square roots using our rule.

√(4 × 27) = √(4) × √(27)

Next, we evaluate √(4) as 2.

√(4) × √(27) = 2 × √(27)

Now, we start over for √(27). We can rewrite 27 as 9 × 3, where 9 is a perfect square, then take it through our steps.

√(108) = 2 × √(27) = 2 × √(9 × 3) = 2 × √(9) × √(3) = 2 × 3 × √(3) = 6 √(3)


tysm..#gozmit

Answer 2

Hey mate!

Here's your answer!!

Here are some steps.

First, we rewrite 108 as a product of a perfect square and another number. Notice that 108 is divisible by 4, and 4 is a perfect square, so we can rewrite 108 as 4 × 27.

√(108) = √(4 × 27)
Now, write the square root as a product of square roots using our rule.

√(4 × 27) = √(4) × √(27)
Next, we evaluate √(4) as 2.

√(4) × √(27) = 2 × √(27)
Now, we start over for √(27). We can rewrite 27 as 9 × 3, where 9 is a perfect square, then take it through our steps.

√(108) = 2 × √(27) = 2 × √(9 × 3) = 2 × √(9) × √(3) = 2 × 3 × √(3) = 6 × √(3)

Since 3 doesn't have any perfect square factors, √(3) is as simplified as possible, so we have that the square root of 108 in radical form is 6 × √(3), or 6√(3).

$hope \: it \: helps \: you.$
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