How to Multiply Square roots?

Last Updated : 23 Jul, 2025

Answer: To multiply square roots, multiply the numbers inside the square roots together and simplify if possible.

Explanation:

To multiply square roots, follow these steps:

  1. Multiply the numbers inside the square roots: Multiply the numbers or expressions inside the square roots together. If there are variables or constants inside the square roots, multiply them as you would normally.
  2. Combine the terms: If there are like terms inside the square roots, combine them. For example, if you have √(a) * √(a), it equals √(a * a) = √(a^2).
  3. Simplify the result: If possible, simplify the expression further. This may involve simplifying any perfect squares or reducing the expression to its simplest form.

For example, let's multiply √(3) by √(5):

  1. Multiply the numbers inside the square roots: √(3) * √(5) = √(3 * 5) = √(15).
  2. There are no like terms to combine in this case.
  3. √(15) is the simplified result. Since 15 is not a perfect square, we cannot simplify it further.

Another example, let's multiply √(4) by √(9):

  1. Multiply the numbers inside the square roots: √(4) * √(9) = √(4 * 9) = √(36).
  2. There are no like terms to combine.
  3. √(36) simplifies to 6, because 36 is a perfect square (6 * 6 = 36).

In summary, to multiply square roots, simply multiply the numbers inside the square roots together and simplify the result if possible.

Multiply √5 × √20

Multiply the numbers inside the square roots: √5 × √20 = √(5 × 20) = √100

Take the square root of the result: √100 = 10

So, √5 × √20 = 10.

Multiply √8 × √27

Multiply the numbers inside the square roots: √8 × √27 = √(8 × 27) = √216

Take the square root of the result: √216 ≈ 14.70 (or simplify to 6√6)

So, √8 × √27 ≈ 14.70 or 6√6.

How do you multiply √3 × √12 and simplify the result?

Multiply the numbers inside the square roots: √3 × √12 = √(3 × 12) = √36

Take the square root of the result: √36 = 6

So, √3 × √12 = 6.

If you need to find the area of a square with side length √8 units, what is the area?

Calculate the area: (√8)² = 8

So, the area of the square is 8 square units.

How do you find the product of √2 × √18 if calculating the volume of a cube where each edge is √2 units long?

Multiply the numbers inside the square roots: √2 × √18 = √(2 × 18) = √36

Take the square root of the result: √36 = 6

So, the product is 6.

Can you multiply square roots with coefficients?

Yes, multiply the coefficients and the square roots separately. For example, 3√2 × 4√5: 3 × 4 × √(2 × 5) = 12√10

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