Simplify. Assume d is greater than or equal to zero. sqrt 54d ______

Factorize and Simplify: sqrt(54d) First, we need to factor 54 into its prime factors and then simplify the square root. Prime factorization of 54 is 2 * 3 * 3 * 3. sqrt(54d) = sqrt(2 * 3 * 3 * 3 * d)Group and Simplify: sqrt(2 * 3 * 3 * 3 * d) Now, group the identical factors and use the exponents to simplify. sqrt(2 * 3^3 * d) = sqrt(2 * 3^2 * 3 * d)Apply Product Property: sqrt(2 * 3^2 * 3 * d) Apply the product property of radicals to separate the perfect square from the rest. sqrt(2 * 3^2 * 3 * d) = sqrt(3^2) * sqrt(2 * 3 * d)Cancel Squares: sqrt(3^2) * sqrt(2 * 3 * d) Since the square root and the square cancel each other out, we can simplify further. sqrt(3^2) * sqrt(2 * 3 * d) = 3 * sqrt(2 * 3 * d)Simplify Inside Square Root: 3 * sqrt(2 * 3 * d) Simplify the expression inside the square root. 3 * sqrt(2 * 3 * d) = 3 * sqrt(6d)Final Simplification: Final Simplification The final simplified form of the square root of 54d is: 3 * sqrt(6d)

Resources

Testimonials

Plans

Resources

Testimonials

Plans

AI tutor

Welcome to Bytelearn!

Let’s check out your problem:

Simplify. Assume $d$ is greater than or equal to zero. $\newline$ $\sqrt{54d}$

View step-by-step help

Home

Math Problems

Algebra 1

Simplify radical expressions: mixed review

Full solution

Q. Simplify. Assume

d

is greater than or equal to zero.

\newline

\sqrt{54d}

Factorize and Simplify: $\sqrt{54d}$ $\newline$ First, we need to factor $54$ into its prime factors and then simplify the square root. $\newline$ Prime factorization of $54$ is $2 \times 3 \times 3 \times 3$ . $\newline$ $\sqrt{54d} = \sqrt{2 \times 3 \times 3 \times 3 \times d}$
Group and Simplify: $\sqrt{2 \times 3 \times 3 \times 3 \times d}$ $\newline$ Now, group the identical factors and use the exponents to simplify. $\newline$ $\sqrt{2 \times 3^3 \times d} = \sqrt{2 \times 3^2 \times 3 \times d}$
Apply Product Property: $\sqrt{2 \times 3^2 \times 3 \times d}$ $\newline$ Apply the product property of radicals to separate the perfect square from the rest. $\newline$ $\sqrt{2 \times 3^2 \times 3 \times d} = \sqrt{3^2} \times \sqrt{2 \times 3 \times d}$
Cancel Squares: $\sqrt{3^2} \times \sqrt{2 \times 3 \times d}$ $\newline$ Since the square root and the square cancel each other out, we can simplify further. $\newline$ $\sqrt{3^2} \times \sqrt{2 \times 3 \times d} = 3 \times \sqrt{2 \times 3 \times d}$
Simplify Inside Square Root: $3 \times \sqrt{2 \times 3 \times d}$ $\newline$ Simplify the expression inside the square root. $\newline$ $3 \times \sqrt{2 \times 3 \times d} = 3 \times \sqrt{6d}$
Final Simplification: Final Simplification $\newline$ The final simplified form of the square root of $54d$ is: $\newline$ $3 \times \sqrt{6d}$