What is (8sqrt(20))/(2-7sqrt(2)) ?

The solution to (8sqrt(20))/(2-7sqrt(2)) is -((16+56sqrt(2))sqrt(5))/(47)

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simplify (8sqrt(20))/(2-7sqrt(2))

simplify

\frac{8 20}{2 - 7 2}

- \frac{( 16 + 56 2 ) 5}{47}

Decimal Notation

- 4.52903 \dots

Solution steps

\frac{8 20}{2 - 7 2}

Multiply by the conjugate

\frac{2 + 7 2}{2 + 7 2}

= \frac{8 ( 2 + 7 2 ) 20}{( 2 - 7 2 ) ( 2 + 7 2 )}

Expand

8 (2 + 72) : 16 + 562

Expand

(2 - 72) (2 + 72) : - 94

= \frac{( 16 + 56 2 ) 20}{- 94}

Factor

20 : 25

= \frac{( 16 + 56 2 ) \cdot 2 5}{- 94}

Factor the number:

94 = 2 \cdot 47

= \frac{( 16 + 56 2 ) \cdot 2 5}{- 2 \cdot 47}

Cancel the common factor:

2

= \frac{( 16 + 56 2 ) 5}{- 47}

Apply the fraction rule:

\frac{a}{- b} = - \frac{a}{b}

= - \frac{( 16 + 56 2 ) 5}{47}

(z^{3})^{2}

\frac{2}{3} + \frac{5}{12}

- 2 9 y + 10 y

\frac{7 ( x ^{2} + x - 6 )}{( x ^{2} - 4 x + 4 ) ( x ^{2} - 9 )}

8 (- 3)

What is (8sqrt(20))/(2-7sqrt(2)) ?
The solution to (8sqrt(20))/(2-7sqrt(2)) is -((16+56sqrt(2))sqrt(5))/(47)