What is (20)/(5sqrt(7)-2\sqrt{5)} ?

The solution to (20)/(5sqrt(7)-2\sqrt{5)} is (4(5sqrt(7)+2sqrt(5)))/(31)

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simplify (20)/(5sqrt(7)-2\sqrt{5)}

simplify

\frac{20}{5 7 - 2 5}

\frac{4 ( 5 7 + 2 5 )}{31}

Decimal Notation

2.28398 \dots

Solution steps

\frac{20}{5 7 - 2 5}

Multiply by the conjugate

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

= \frac{20 ( 5 7 + 2 5 )}{( 5 7 - 2 5 ) ( 5 7 + 2 5 )}

Expand

20 (57 + 25) : 1007 + 405

Expand

(57 - 25) (57 + 25) : 155

= \frac{100 7 + 40 5}{155}

Factor out common term

20 : 20 (57 + 25)

= \frac{20 ( 5 7 + 2 5 )}{155}

Factor the number:

20 = 5 \cdot 4

= \frac{5 \cdot 4 ( 5 7 + 2 5 )}{155}

Factor the number:

155 = 5 \cdot 31

= \frac{5 \cdot 4 ( 5 7 + 2 5 )}{5 \cdot 31}

Cancel the common factor:

5

= \frac{4 ( 5 7 + 2 5 )}{31}

\frac{2 ^{3}}{2 ^{6}}

+ 49 r^{2} - 64

5 x 4^{3}

\frac{7}{3}

(2 + i) (3 + i)

What is (20)/(5sqrt(7)-2\sqrt{5)} ?
The solution to (20)/(5sqrt(7)-2\sqrt{5)} is (4(5sqrt(7)+2sqrt(5)))/(31)