Question

Please help me out guys!I just reached in class 9...Classes are not started... trying out onmy own...so I need to check whether my answeris correct or not... I got "115"...is it correct?
show step by step please.​

Answer 1

Answer:

19√5 + 5√2

Step-by-step explanation:

= > 8√45 - √125 + √200 - √50

Here,

√45 = √( 5 x 3 x 3 ) = √( 5 x 3^2 ) = 3√5

√125 = √( 5 x 5 x 5 ) = √( 5^2 x 5 ) = 5√5

√200 = ( 2 x 10 x 10 ) = √( 2 x 10^2 ) = 10√2

√50 = √( 5 x 5 x 2 ) = √( 5^2 x 2 ) = 5√2

Now,

= > 8( 3√5 ) - 5√5 + 10√2 - 5√2

= > 24√5 - 5√5 + 10√2 - 5√2

= > 19√5 + 5√2.

Hence the correct simplification is 19√5 + 5√2

Answer 2

${\boxed{\boxed{\mathtt{Answer}}}}$

→ 19√5 + 5√2

${\boxed{\boxed{\mathtt{Solution}}}}$

$\mathtt{(8\:\times\sqrt{45})\:-\:\sqrt{125}\:+\:\sqrt{200}\:-\:\sqrt{50}}$

$\mathtt{\implies \: \sqrt{45}\:=\: \sqrt{3\:\times3\:\times\:5}}$

$\mathtt{\implies\:\sqrt{125}\:=\:\sqrt{5\:\times5\:\times\:5}}$

$\mathtt{\implies\:\sqrt{200}\:=\:\sqrt{2\:\times2\:\times\:2\:\times5\:\times5}}$

$\mathtt{\implies\:\sqrt{50}\:=\:\sqrt{2\:\times5\:\times5}}$

Now putting these values in the Question :-

$\implies \: 8( \sqrt{3 \times 3 \times 5} ) \: - \: \sqrt{5 \times 5 \times 5} \: + \: \sqrt{2 \times 2 \times 2 \times 5 \times 5} \: - \: \sqrt{2 \times 5 \times 5}$

$\implies \: 8 \times 3 \sqrt{5} - 5 \sqrt{5} + 2 \times 5 \sqrt{2 } - 5 \sqrt{2}$

$\mathtt{\implies\:24\:\sqrt{5}\:-\:5\sqrt{5}\:+\:10\sqrt{2}\:-\:5\sqrt{2}}$

$\mathtt{\implies \: \sqrt{5}\times(24-5)\:+\:\sqrt{2}\times(10-5)}$

$\mathtt{\red{\implies\:19\sqrt{5}\:-\:5\sqrt{2}}}$