Rationalize the denominator. displaystylefrac{sqrt{{40}}}{sqrt{{56}}}

Rationalize the denominator. displaystylefrac{sqrt{{40}}}{sqrt{{56}}}

Question
Rationalize the denominator.
\(\displaystyle\frac{\sqrt{{40}}}{\sqrt{{56}}}\)

Answers (1)

2021-01-11
Step 1
We write them under one radical. Then recue \(\displaystyle\frac{40}{{56}}\) by 8.
\(\displaystyle=\frac{\sqrt{{40}}}{\sqrt{{56}}}\)
\(\displaystyle=\sqrt{{\frac{40}{{56}}}}\)
\(\displaystyle=\sqrt{{\frac{{{40}\div{8}}}{{{56}\div{8}}}}}\)
\(\displaystyle=\sqrt{{\frac{5}{{7}}}}\)
Step 2
Separate the radicals. And multiply numerator and denominator by \(\sqrt{7}\)
\(\displaystyle\sqrt{{\frac{5}{{7}}}}\)
\(\displaystyle=\frac{\sqrt{{5}}}{\sqrt{{7}}}\)
\(\displaystyle=\frac{{\sqrt{{5}}\times\sqrt{{7}}}}{{\sqrt{{7}}\times\sqrt{{7}}}}\)
\(\displaystyle==\frac{\sqrt{{{35}}}}{{7}}\)
Answer: \(\displaystyle\frac{\sqrt{{{35}}}}{{7}}\)
0

Relevant Questions

asked 2020-12-12
To rationalize:
Each numerator. Assume that variables represent positive real numbers.
Given: An expression : \(\displaystyle\frac{{\sqrt[{{3}}]{{9}}}}{{7}}.\)
asked 2020-11-02
To calculate:
To rationalize the denominator of the expression \(\displaystyle{\frac{{\sqrt{{{5}}}\ -\ \sqrt{{{2}}}}}{{\sqrt{{{5}}}\ +\ \sqrt{{{2}}}}}}.\)
asked 2021-01-22
Find the rationalize the denominator of \(\frac{-4}{\sqrt[3]{5x}}\)
asked 2020-12-16
To calculate: The simplified form of the expression \(\displaystyle\frac{\sqrt{{12}}}{\sqrt{{{x}+{1}}}}.\)
asked 2020-12-13
To calculate:
The expression \(\displaystyle\frac{{2.7}^{{-{11}\text{/}{12}}}}{{2.7}^{{-{1}\text{/}{6}}}}\) with positive exponent.
asked 2021-02-21
Perform the indicated operation and express all answers with a rational denominator \(2a^{2}b\sqrt[3]{4a^{3}b}\ \cdot\ -6ab^{2}\sqrt[3]{18ab^{4}}\)
asked 2020-11-23
To multiply:
The given expression. Then simplify if possible. Assume that all variables represent positive real numbers.
Given:
An expression: \(\displaystyle\sqrt{{3}}{\left(\sqrt{{27}}-\sqrt{{3}}\right)}\)
asked 2021-01-05
The simplified form of the expression
\(\displaystyle{\sqrt[{{4}}]{{{c}{d}^{2}}}}\times{\sqrt[{{3}}]{{{c}^{2}{d}}}}.\)
asked 2021-02-08
Combining radicals simplify the expression. Assume that all letters denote positive numbers.
\(\displaystyle\sqrt{{{16}{x}}}+\sqrt{{{x}^{5}}}\)
asked 2020-11-08
To simplify:
The given redical:
An expression: \(\displaystyle{\sqrt[{{4}}]{{{\left({x}^{2}-{4}\right)}^{4}}}}.\)
Use absolute value bars when necessary.
...