# What happens when you multiply a square root by a fraction?

## What happens when you multiply a square root by a fraction?

Step 1: Multiply numerator and denominator by a radical that will get rid of the radical in the denominator. If the radical in the denominator is a square root, then you multiply by a square root that will give you a perfect square under the radical when multiplied by the denominator.

### What is the rule for multiplying square roots?

To multiply two square roots, we just multiply the radicands and put the product under a radical sign. That is, the product of two square roots is equal to the square root of the product of the radicands.

#### Do square roots cancel when multiplied?

We can say that the square root and the square cancel each other out. They are the inverse of each other. If we have a number written with the index 2 ( squared) then taking the square root simply means that we leave out the 2 ( this only applies to positive numbers ).

Do you add square roots when multiplying?

You can multiply square roots, a type of radical expression, just as you might multiply whole numbers. Sometimes square roots have coefficients (an integer in front of the radical sign), but this only adds a step to the multiplication and does not change the process.

Do square roots cancel eachother out in a fraction?

Most square roots are irrational numbers. This means we can’t give their exact value in fractions or decimals.

## Can you have a square root on the bottom of a fraction?

When we have a fraction with a root in the denominator, like 1/√2, it’s often desirable to manipulate it so the denominator doesn’t have roots. To do that, we can multiply both the numerator and the denominator by the same root, that will get rid of the root in the denominator.

### What is the easiest way to multiply fractions?

Multiply the top numbers (the numerators ).

• Multiply the bottom numbers (the denominators ).
• Simplify the fraction if needed.
• #### How do you simplify the square root of a fraction?

Find the square root of √ (144 ÷ 81)? Solution: Given the number is √ (144 ÷ 81).

• Evaluate √ (256 ÷ 64)? Solution: Given the number is √ (256 ÷ 64).
• Evaluate √ (49 ÷ 121)? Solution: Given the number is √ (49 ÷ 121).
• Evaluate √ (25 ÷ 169)? Solution: Given the number is √ (25 ÷ 169).
• Find the value of √ (196 ÷ 9)?
• Find out the value of √25 × √16?
• How do you find the square roots of fractions?

Ask for help. If you are experiencing difficulty when calculating the square root of a fraction,try asking a friend or colleague for help.

• Double-check your work. When calculating a square root of a fraction,it’s important to double-check your math to ensure you are getting the correct answers.
• Practice.
• How to add square roots to numerator fractions?

– For example: ( 12 / 16) 2 – 12 and 16 can both be divided by 4. 12/4 = 3 and 16/4 = 4; therefore, 12 / 16 reduces to 3 / 4. – Now, you will square the fraction 3 / 4. – ( 3 / 4) 2 = 9 / 16, which cannot be reduced. – To prove this, let’s square the original fraction without reducing: ( 12 / 16) 2 = ( 12 x 12 / 16 x 16) = ( 144 / 256) (