Simplify. sqrt (63/4) ______

Apply quotient rule of radicals: Apply the quotient rule of radicals to sqrt(63/4). The quotient rule states that the square root of a quotient is equal to the quotient of the square roots of the numerator and the denominator. Therefore, sqrt(63/4) can be written as sqrt(63) / sqrt(4).Simplify square root of 63: Simplify sqrt(63). To simplify the square root of a number, look for perfect square factors. The prime factorization of 63 is 3 * 3 * 7, which contains a pair of 3's. Extract the square root of the pair of 3's to get 3, and leave the square root of 7 inside the radical. Thus, sqrt(63) simplifies to 3 * sqrt(7).Simplify square root of 4: Simplify sqrt(4). The number 4 is a perfect square, as it is 2 * 2. The square root of 4 is therefore 2.Combine the results: Combine the results from the previous steps. We have found that sqrt(63) is 3 * sqrt(7) and sqrt(4) is 2. So, sqrt(63/4) is (3 * sqrt(7)) / 2.

Resources

Testimonials

Plans

Resources

Testimonials

Plans

AI tutor

Welcome to Bytelearn!

Let’s check out your problem:

Simplify. $\newline$ $\sqrt{\frac{63}{4}}$ $\newline$ ______

View step-by-step help

Home

Math Problems

Algebra 2

Simplify radical expressions involving fractions

Full solution

Q. Simplify.

\newline

\sqrt{\frac{63}{4}}

\newline

______

Apply quotient rule of radicals: Apply the quotient rule of radicals to $\sqrt{\frac{63}{4}}$ . $\newline$ The quotient rule states that the square root of a quotient is equal to the quotient of the square roots of the numerator and the denominator. $\newline$ Therefore, $\sqrt{\frac{63}{4}}$ can be written as $\frac{\sqrt{63}}{\sqrt{4}}$ .
Simplify square root of $63$ : Simplify $\sqrt{63}$ . $\newline$ To simplify the square root of a number, look for perfect square factors. The prime factorization of $63$ is $3 \times 3 \times 7$ , which contains a pair of $3$ 's. $\newline$ Extract the square root of the pair of $3$ 's to get $3$ , and leave the square root of $7$ inside the radical. $\newline$ Thus, $\sqrt{63}$ simplifies to $3 \times \sqrt{7}$ .
Simplify square root of $4$ : Simplify $\sqrt{4}$ . $\newline$ The number $4$ is a perfect square, as it is $2 \times 2$ . $\newline$ The square root of $4$ is therefore $2$ .
Combine the results: Combine the results from the previous steps. $\newline$ We have found that $\sqrt{63}$ is $3 \cdot \sqrt{7}$ and $\sqrt{4}$ is $2$ . $\newline$ So, $\sqrt{\frac{63}{4}}$ is $\left(3 \cdot \sqrt{7}\right) / 2$ .