MathMaster Blog

Multiplying radicals implies the use of the Product and Quotient rules.

According to the Product Rule, the product of two or more numbers raised to a power equals the product of each number raised to the same power.

Multiplying Radicals Formula 1

The Quotient Rule states that the radical of a quotient is equal to the quotient of the radicals of the numerator and denominator.

Multiplying Radicals Formula 2

When multiplying radicals (with the same index), multiply under the radical first, then in front of it.

Example 1:

Multiply:$5\sqrt{5} \times 3\sqrt{10}$


Multiply out front and multiply under the radicals:

$5\sqrt{5} \times 3\sqrt{10} = 15\sqrt{50}$

Then, simplify the result:

$15\sqrt{50} = 15\sqrt{2 \times 25} = 15\sqrt{2} \times 5\sqrt{2} = 75\sqrt{2}$

Answer: $75\sqrt{2}$