Multiplying Radicals Calculator

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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?

In mathematics, radical is defined as an expression which contains an expression with the radical symbol (√). The number present inside the number is called the radicand whereas the small number which is present outside of the radical symbol is called the index. For example, 3√8. Here 3 is the index, and 8 is the radicand. The radical can be a square root, cube root, or the higher order of nth root. The radicals are generally used to remove the exponents. While multiplying the radicals, it follows the product rule. When the radicals are multiplied with the same index number, multiply the radicand value and then multiply the values in front of the radicals (i.e., coefficients of the radicals). The product rule for the multiplying radicals is given by

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

Multiplying Radicals Examples

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.

Also, check: Radical

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

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