Simplify. sqrt 28 ______

Find Prime Factors: sqrt(28) Let's find the prime factors of the radicand (the number inside the square root). Prime factorization of a number is expressing it as the product of its prime factors. sqrt(28) = sqrt(2 * 2 * 7)Group and Combine Factors: sqrt(2 * 2 * 7) Now, group the identical factors. Combine the identical factors by using the exponents. sqrt(2 * 2 * 7) = sqrt(2^2 * 7)Apply Product Property: sqrt(2^2 * 7) Apply the product property of radicals: sqrt(a * b) = sqrt(a) * sqrt(b) sqrt(2^2 * 7) = sqrt(2^2) * sqrt(7)Simplify Perfect Square: sqrt(28) = sqrt(2^2) * sqrt(7) Simplify the square root of the perfect square. Square and square root cancel each other out. sqrt(2^2) * sqrt(7) = 2 * sqrt(7)

Resources

Testimonials

Plans

Resources

Testimonials

Plans

AI tutor

Welcome to Bytelearn!

Let’s check out your problem:

Simplify. $\newline$ $\sqrt{28}$

View step-by-step help

Home

Math Problems

Algebra 1

Simplify radical expressions: mixed review

Full solution

Q. Simplify.

\newline

\sqrt{28}

Find Prime Factors: $\sqrt{28}$ $\newline$ Let's find the prime factors of the radicand (the number inside the square root). $\newline$ Prime factorization of a number is expressing it as the product of its prime factors. $\newline$ $\sqrt{28} = \sqrt{2 \times 2 \times 7}$
Group and Combine Factors: $\sqrt{2 \times 2 \times 7}$ $\newline$ Now, group the identical factors. $\newline$ Combine the identical factors by using the exponents. $\newline$ $\sqrt{2 \times 2 \times 7} = \sqrt{2^2 \times 7}$
Apply Product Property: $\sqrt{2^2 \times 7}$ $\newline$ Apply the product property of radicals: $\newline$ $\sqrt{a \times b} = \sqrt{a} \times \sqrt{b}$ $\newline$ $\sqrt{2^2 \times 7} = \sqrt{2^2} \times \sqrt{7}$
Simplify Perfect Square: $\sqrt{28} = \sqrt{2^2} \times \sqrt{7}$ $\newline$ Simplify the square root of the perfect square. $\newline$ Square and square root cancel each other out. $\newline$ $\sqrt{2^2} \times \sqrt{7} = 2 \times \sqrt{7}$