Simplify. Assume t is greater than or equal to zero. sqrt 20t^9 ______

Factorize and Identify Perfect Squares: sqrt(20t^9) First, we need to factor the radicand (the number inside the square root) into its prime factors and identify perfect squares. Prime factorization of 20 is 2 * 2 * 5, and we can express t^9 as (t^4)^2 * t. sqrt(20t^9) = sqrt(2 * 2 * 5 * (t^4)^2 * t)Group Identical Factors: sqrt(2 * 2 * 5 * (t^4)^2 * t) Now, group the identical factors and the perfect squares. sqrt(2 * 2 * 5 * (t^4)^2 * t) = sqrt(2^2 * 5 * (t^4)^2 * t)Apply Product Property of Radicals: sqrt(2^2 * 5 * (t^4)^2 * t) Apply the product property of radicals, which allows us to take the square root of each factor separately. sqrt(2^2 * 5 * (t^4)^2 * t) = sqrt(2^2) * sqrt(5) * sqrt((t^4)^2) * sqrt(t)Simplify Perfect Squares: sqrt(2^2) * sqrt(5) * sqrt((t^4)^2) * sqrt(t) Simplify the square roots of the perfect squares. sqrt(2^2) * sqrt(5) * sqrt((t^4)^2) * sqrt(t) = 2 * sqrt(5) * t^4 * sqrt(t)Combine Terms Inside Square Root: 2 * sqrt(5) * t^4 * sqrt(t) Combine the terms outside the square root with the terms inside the square root. 2 * t^4 * sqrt(5) * sqrt(t) = 2t^4 * sqrt(5t)

Resources

Testimonials

Plans

Resources

Testimonials

Plans

AI tutor

Welcome to Bytelearn!

Let’s check out your problem:

Simplify. Assume $t$ is greater than or equal to zero. $\newline$ $\sqrt{20t^9}$

View step-by-step help

Home

Math Problems

Algebra 1

Simplify radical expressions: mixed review

Full solution

Q. Simplify. Assume

t

is greater than or equal to zero.

\newline

\sqrt{20t^9}

Factorize and Identify Perfect Squares: $\sqrt{20t^9}$ $\newline$ First, we need to factor the radicand (the number inside the square root) into its prime factors and identify perfect squares. $\newline$ Prime factorization of $20$ is $2 \times 2 \times 5$ , and we can express $t^9$ as $(t^4)^2 \times t$ . $\newline$ $\sqrt{20t^9} = \sqrt{2 \times 2 \times 5 \times (t^4)^2 \times t}$
Group Identical Factors: $\sqrt{2 \times 2 \times 5 \times (t^4)^2 \times t}$ Now, group the identical factors and the perfect squares. $\sqrt{2 \times 2 \times 5 \times (t^4)^2 \times t} = \sqrt{2^2 \times 5 \times (t^4)^2 \times t}$
Apply Product Property of Radicals: $\sqrt{2^2 \cdot 5 \cdot (t^4)^2 \cdot t}$ Apply the product property of radicals, which allows us to take the square root of each factor separately. $\sqrt{2^2 \cdot 5 \cdot (t^4)^2 \cdot t} = \sqrt{2^2} \cdot \sqrt{5} \cdot \sqrt{(t^4)^2} \cdot \sqrt{t}$
Simplify Perfect Squares: $\sqrt{2^2} \times \sqrt{5} \times \sqrt{(t^4)^2} \times \sqrt{t}$ $\newline$ Simplify the square roots of the perfect squares. $\newline$ $\sqrt{2^2} \times \sqrt{5} \times \sqrt{(t^4)^2} \times \sqrt{t} = 2 \times \sqrt{5} \times t^4 \times \sqrt{t}$
Combine Terms Inside Square Root: $2 \times \sqrt{5} \times t^4 \times \sqrt{t}$ $\newline$ Combine the terms outside the square root with the terms inside the square root. $\newline$ $2 \times t^4 \times \sqrt{5} \times \sqrt{t} = 2t^4 \times \sqrt{5t}$