Multiplying The Square Root Calculator

Multiplying square roots is a fundamental operation in algebra that combines two square roots into a single expression. This calculator helps you perform this operation quickly and accurately, with clear explanations of the underlying mathematics.

How to Use This Calculator

To multiply two square roots, enter the radicands (the numbers inside the square roots) into the calculator fields. The calculator will automatically compute the product of the square roots and simplify the result when possible.

For example, if you want to multiply √8 and √18, enter 8 in the first field and 18 in the second field. The calculator will show you that √8 × √18 = √(8 × 18) = √144 = 12.

The Formula Explained

The fundamental property of square roots that allows multiplication is:

Square Root Multiplication Formula

√a × √b = √(a × b)

This formula states that the product of two square roots is equal to the square root of the product of the radicands. When the product inside the square root is a perfect square, the square root can be simplified to an integer or simplified radical.

Worked Examples

Let's look at a few examples to see how multiplying square roots works in practice.

Example	Calculation	Result
√9 × √16	√(9 × 16) = √144 = 12	12
√5 × √20	√(5 × 20) = √100 = 10	10
√7 × √28	√(7 × 28) = √196 = 14	14

In each case, the product of the square roots simplifies to a whole number because the product of the radicands is a perfect square.

Frequently Asked Questions

Can I multiply more than two square roots at once?

Yes, the property of square roots extends to any number of square roots. For example, √a × √b × √c = √(a × b × c).

What if the radicands are not perfect squares?

If the product of the radicands is not a perfect square, the result will remain in the form of a square root. For example, √2 × √3 = √6.

Is there a difference between multiplying square roots and adding them?

Yes, square roots cannot be added directly. For example, √a + √b cannot be simplified further unless a and b are perfect squares and equal.