Square root of 10 times square root of 50 (√10 × √50)

Square root of 10 times square root of 50

If you're looking for the answer to square root of 10 times square root of 50 in its simplest form and in decimal form, you have come to the right place. Here are step-by-step instructions to calculate square root of 10 times square root of 50.

Step 1: Setup
We start by showing you how to write square root of 10 times square root of 50 mathematically, so it is easy to follow along. Note that the square root symbol (√) is called a radical, and the number inside the radical is called a radicand. Here is what we want to solve:

√10 × √50

Step 2: Multiply together
It is easy to multiply two square roots together, such as √10 × √50. This will result in just one radical and one radicand. Here is the formula and the math:

√a × √b = √a × b

√10 × √50 = √10 × 50

√500

Step 3: List factors of radicand
Now we will list all the factors of the radicand from the previous step.

Factors of 500: 1, 2, 4, 5, 10, 20, 25, 50, 100, 125, 250, 500.

Step 4: Find largest perfect square
We now need to find the largest perfect square from the factors we listed above. If the square root of a number is an integer, then the number is a perfect square. The largest perfect square (LPS) from the list above is as follows:

LPS: 100

Step 5: Calculate simplest radical form
To simplify the result from Step 2, we divide the radicand by the LPS to get the new radicand. The square root of the LPS becomes the outside number to the left of the radical. Here is the formula and the math, where R refers to the radicand:

(√LPS)√R ÷ LPS

(√100)√500 ÷ 100

10√5

Step 5: Calculate decimal answer
The decimal answer to √10 × √50 is simply the square root of the product we got from Step 2.

√500 ≈ 22.360680

That's it. Now we have the square root of 10 times the square root of 50 in its simplest form and in decimal form:

√10 × √50

= 10√5 ≈ 22.360680

Multiplying Square Roots Calculator
Use the calculator below to multiply together another set of square roots.

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