Question

answer=5.398 show the process in picture only​

Answer 1

Hope it will help you....

Answer 2

$\dfrac{15}{ \sqrt{10} + \sqrt{20} + \sqrt{40} - \sqrt{5} - \sqrt{80} }$

$= \dfrac{15}{3.162 + (\sqrt{5} \times \sqrt{4} ) + ( \sqrt{4} \times \sqrt{10}) - 2.162 - ( \sqrt{5} \times \sqrt{16}) }$

[Since √20 can be written as √5 * √4 and √40 can be written as √4 * √10 and √80 can be written as √16 * √5]

$= \dfrac{15}{3.162 +2 \sqrt{5} + 2 \sqrt{10} - 2.236 - 4 \sqrt{5} }$

[Since √4 = 2 and √16 = 4]

$= \dfrac{15}{3.162 + 2(2.236) + 2(3.162) - 2.236 - 4(2.236)}$

[Since given that √5 = 2.236 , √10 = 3.162]

$= \dfrac{15}{0.926 + 4.472 + 6.324 - 8.944}$

[Above 3.162 - 2.236 = 0.926]

$= \dfrac{15}{5.398 + 6.324 - 8.944}$

[Above 0.926 + 4.472 = 5.398]

$= \dfrac{15}{11.722 - 8.944}$

[Above 5.398 + 6.324 = 11.722]

$= \dfrac{15}{2.778}$

[Above 11.722 - 8.944 = 2.778]

$= \dfrac{15 \times 1000}{2.778 \times 1000}$

[Above I multiplied by 1000 both numerator and denominator to eliminate the decimal]

$= \dfrac{15000}{2778}$

$= \dfrac{7500}{1389}$

[Above both numerator and denominator are divided by 2 i.e, 15000/2 = 7500, 2778/2 = 1389]

$= \dfrac{2500}{463}$

[ Above both numerator and denominator are divided by 3 i.e, 7500/3 = 2500, 1398/3 = 463]

$=5.399568035$

$= 5.398(approx)$