i need help with these questions

simplify √4x^2/y^3
√2x^4/72
√18+√32

√31(√3+√27)

hint:

√n^2 = n

√n^4 = n^2

√ab = √a√b

i didn't get what u mean can u explain more if u can please ?

Let's break down each question and explain how to get the answer.

1. Simplify √(4x^2/y^3):

To simplify this expression, we need to understand that square roots can be separated. We can take the square root of the numerator and the denominator separately.

√(4x^2/y^3) = √(4x^2)/√(y^3)

Now let's simplify each square root separately:

√(4x^2) = 2x

And √(y^3) = y * √y

So, the simplified expression is 2x / (y * √y)

2. Simplify √(2x^4/72):

For this expression, we are simplifying a fraction within the square root. To simplify, we can divide the numerator and denominator by the greatest common divisor (GCD).

The GCD of 2, x^4, and 72 is 2. So, dividing both the numerator and denominator by 2:

√(2x^4/72) = √(x^4/36)

Now we can simplify the expression inside the square root:

√(x^4/36) = (x^4)^(1/2) / 36^(1/2)

Since the square root of x^4 is x^2 and the square root of 36 is 6, we have:

(x^2)/6

Therefore, the simplified expression is (x^2)/6.

3. Simplify √(18) + √(32):

In this expression, we are adding two square roots. We can simplify each square root separately before adding them together.

√(18) = √(9 * 2) = 3√2

√(32) = √(16 * 2) = 4√2

Now we can add them together:

3√2 + 4√2 = (3 + 4)√2 = 7√2

Therefore, the simplified expression is 7√2.

4. Simplify √(31(√3 + √27)):

First, we simplify the square root of 27:

√27 = √(9 * 3) = 3√3

Now let's substitute this value back into the expression:

√(31(√3 + 3√3)) = √(31 * 4√3) = √(124√3)

To simplify further, we can separate the square root:

√(124√3) = √124 * √(√3) = √4 * √31 * √(√3)

Simplifying further:

√4 = 2
√31 = √31
√(√3) = (3)^(1/4)

So, the simplified expression is 2√31 * (3)^(1/4).

I hope this helps you understand how to simplify these square root expressions!