What is (sqrt(5)+sqrt(2))/(7+2sqrt(10)) ?

The solution to (sqrt(5)+sqrt(2))/(7+2sqrt(10)) is (sqrt(5)-sqrt(2))/3

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

simplify (sqrt(5)+sqrt(2))/(7+2sqrt(10))

simplify

\frac{5 + 2}{7 + 2 10}

\frac{5 - 2}{3}

Decimal Notation

0.27395 \dots

Solution steps

\frac{5 + 2}{7 + 2 10}

Multiply by the conjugate

\frac{7 - 2 10}{7 - 2 10}

= \frac{( 5 + 2 ) ( 7 - 2 10 )}{( 7 + 2 10 ) ( 7 - 2 10 )}

Expand

(5 + 2) (7 - 210) : 35 - 32

Expand

(7 + 210) (7 - 210) : 9

= \frac{3 5 - 3 2}{9}

Factor out common term

3

= \frac{3 ( 5 - 2 )}{9}

Factor the number:

9 = 3 \cdot 3

= \frac{3 ( 5 - 2 )}{3 \cdot 3}

Cancel the common factor:

3

= \frac{5 - 2}{3}

10 lo g_{10} (4)

\frac{42}{48}

(a^{4})^{5}

- (\frac{1}{2})^{5}

2 7^{- 3^{- 1}}

What is (sqrt(5)+sqrt(2))/(7+2sqrt(10)) ?
The solution to (sqrt(5)+sqrt(2))/(7+2sqrt(10)) is (sqrt(5)-sqrt(2))/3