Resources

Resources

Bytelearn - cat image with glasses

AI tutor

Welcome to Bytelearn!

Let’s check out your problem:

Simplify. Assume $b$ is greater than or equal to zero. $\newline$ $\sqrt{75b^3}$

View step-by-step help

View step-by-step help

Simplify radical expressions with variables

Full solution

Q. Simplify. Assume

b

is greater than or equal to zero.

\newline

\sqrt{75b^3}

Factorize Perfect Squares: Factorize $75b^3$ to find perfect squares. $\newline$ The prime factorization of $75$ is $3 \times 5 \times 5$ , and $b^3$ is $b \times b \times b$ . So, $75b^3$ can be written as $3 \times 5^2 \times b^2 \times b$ .
Group Perfect Squares: Group the perfect squares under the square root. $\newline$ We have $\sqrt{75b^3} = \sqrt{3 \times 5^2 \times b^2 \times b}$ . $\newline$ The perfect squares are $5^2$ and $b^2$ , which can be taken out of the square root.
Simplify Square Root: Simplify the square root by taking out the perfect squares. Taking the square root of the perfect squares gives us $5b$ , and we are left with $\sqrt{3b}$ inside the radical. So, $\sqrt{75b^3} = 5b \times \sqrt{3b}$ .

More problems from Simplify radical expressions with variables

Question

\newline

\sqrt{\frac{9}{25}}

\newline

Posted 3 months ago

Question

\newline

1,000

\text{ milligrams}

\_\_\_\_

\text{ grams}

Posted 3 months ago

Question

3

-gallon bottle of bleach costs

\$11.52

. What is the price per quart?

\newline

Posted 3 months ago

Question

Maureen can't wait to make chocolate chip zucchini bread with zucchini from her garden. Her recipe calls for

8

ounces of chocolate chips per loaf. If she has enough zucchini to make

4

loaves of zucchini bread, how many pounds of chocolate chips does she need?

\newline

Hint: There are

16

1

\newline

Write your answer as a whole number, decimal, or simplified fraction. Do not round.

\newline

Posted 3 months ago

Question

A whale is swimming due north at a speed of

30

miles per hour. Just

5

miles away, a whale-watching tour boat is traveling south, directly toward the whale, at a speed of

46

miles per hour. How long will it be before they meet? If necessary, round your answer to the nearest minute.

\_\_\_\_

\_\_\_\_

Posted 3 months ago

Question

\newline

500

=

Posted 4 months ago

Question

\newline

2,000

=

Posted 4 months ago

Question

\newline

750

=

Posted 4 months ago

Question

\newline

1,500

=

Posted 4 months ago

Question

\newline

1,500

=

Posted 4 months ago