Simplified Square Root Of 150

Square Root of 150 How to Find the Square Root of 150? En from en.asriportal.com

Understanding Square Root

In mathematics, a square root of a number is another number that, when multiplied by itself, gives the original number. For example, the square root of 16 is 4 because 4 multiplied by 4 equals 16. The symbol used for square root is √.

Square Root of 150

To simplify the square root of 150, we need to find the factors of 150. The factors of 150 are 1, 2, 3, 5, 6, 10, 15, 25, 30, 50, 75, and 150. We can then group the factors into pairs, where one number is a perfect square. In this case, we can group 25 and 6 together, leaving us with 25 multiplied by 6 outside of the square root symbol:

√150 = √(25 x 6)

Further Simplification

We can simplify √(25 x 6) by taking the square root of 25, which is 5, and multiplying it by the square root of 6:

√(25 x 6) = 5√6

Therefore, the simplified square root of 150 is 5√6.

Why Simplify Square Roots?

Simplifying square roots makes them easier to work with in mathematical equations. It also helps to identify common factors that can be cancelled out, making the equation simpler to solve.

Common Square Roots

It is helpful to memorize the square roots of common numbers. For example, the square root of 4 is 2, the square root of 9 is 3, and the square root of 16 is 4. These common square roots can be used to simplify more complex square roots.

Practice Problems

Here are some practice problems to further improve your understanding of simplifying square roots:

√12 = ?

√48 = ?

√75 = ?

Solution to Practice Problems

To solve the practice problems, we need to find the factors of the given numbers and group them into pairs:

√12 = √(4 x 3) = 2√3

√48 = √(16 x 3) = 4√3

√75 = √(25 x 3) = 5√3

Therefore, the simplified square roots are 2√3, 4√3, and 5√3, respectively.

Conclusion

Simplifying square roots is an important skill in mathematics. It makes equations easier to solve and helps to identify common factors. Practice makes perfect, so keep practicing and memorizing common square roots to improve your skills.