Simplify. Assume f is greater than or equal to zero. sqrt 75f^9 ______

Factor Perfect Squares: Factor the expression under the square root to identify perfect squares. What is the complete factorization of 75f^9? Complete factorization of 75f^9 = 3 * 5^2 * f^8 * fGroup Factors: Group the factors into perfect squares and separate the non-perfect square. sqrt(75f^9) will become sqrt(3 * 5^2 * f^8 * f) What is the expression after making perfect squares inside the radical? sqrt(75f^9) = sqrt(3 * (5^2) * (f^8) * f)Simplify Radical: Simplify the square root of the perfect squares and leave the non-perfect square inside the radical. sqrt(3 * (5^2) * (f^8) * f) = 5 * f^4 * sqrt(3f)Final Expression: Write the final simplified expression. The simplified expression is 5f^4 * sqrt(3f).

Resources

Testimonials

Plans

Resources

Testimonials

Plans

AI tutor

Welcome to Bytelearn!

Let’s check out your problem:

Simplify. Assume $f$ is greater than or equal to zero. $\newline$ $\sqrt{75f^9}$

View step-by-step help

Home

Math Problems

Algebra 1

Simplify radical expressions with variables

Full solution

Q. Simplify. Assume

f

is greater than or equal to zero.

\newline

\sqrt{75f^9}

Factor Perfect Squares: Factor the expression under the square root to identify perfect squares. $\newline$ What is the complete factorization of $75f^9$ ? $\newline$ Complete factorization of $75f^9 = 3 \times 5^2 \times f^8 \times f$
Group Factors: Group the factors into perfect squares and separate the non-perfect square. $\sqrt{75f^9}$ will become $\sqrt{3 \times 5^2 \times f^8 \times f}$ What is the expression after making perfect squares inside the radical? $\sqrt{75f^9} = \sqrt{3 \times (5^2) \times (f^8) \times f}$
Simplify Radical: Simplify the square root of the perfect squares and leave the non-perfect square inside the radical. $\sqrt{3 \times (5^2) \times (f^8) \times f} = 5 \times f^4 \times \sqrt{3f}$
Final Expression: Write the final simplified expression. $\newline$ The simplified expression is $5f^4 \times \sqrt{3f}$ .