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Multiplying Radicals Calculator is a free online tool that displays the product of two radicals. BYJU’S online multiplying radicals calculator tool performs the calculation faster and it displays the multiplication of two radical values in a fraction of seconds.

How to Use the Multiplying Radicals Calculator?

The procedure to use the multiplying radicals calculator is as follows:

Step 1: Enter the coefficient of the radical, index and radicand value in the input field (Example: 2 3√27)

Step 2: Now click the button “Solve” to get the product of two radicals

Step 3: Finally, the multiplication of two radicals will be displayed in the output field (I.e., Multiplying Radicals, 2 3√27 × 2 3√8 =  24)

What is Meant by Multiplying Radicals?

$\sqrt[n]{ab}=\sqrt[n]{a}.\sqrt[n]{b}$

Example 1

Simplify 2 3√27 × 2 3√8

Solution:

Given: 2 3√27 × 2 3√8

Here, both the multiplicand and the multiplier has a radical with the same index number (i,e., 3).

So, by using the product rule, it becomes

2 3√27 × 2 3√8 = 4 3√(27 × 8)

= 4 3√216

Take the cube root of 216, we get

= 4 (6) = 24

Therefore, 2 3√27 × 2 3√8 =  24.

Example 2:

Determine the value of 4 √25 × 2 3√125

Solution:

Given: 4 √25 × 2 3√125

Since the index value of multiplier and the multiplicand are different, simplify the multiplicand and multiplier separately, and then multiply it

We know that √25 = 5, and 3√125 = 5

4 √25 × 2 3√125 = 4 (5)× 2(5)

=20×10

= 200

Hence, 4 √25 × 2 3√125 = 200