An algebra problem by Stuti Malik

Algebra Level 1

Work out without using calculator, evaluate

( ( 9 5 2 − 5 2 ) ÷ 10 ) 0.5 \large {((95^2 - 5^2)\div 10)}^{0.5}


The answer is 30.

Stuti Malik by Stuti Malik , 24, United Kingdom

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5 solutions

[ ( 9 5 2 − 5 2 ) ÷ 10 ] 0.5 [(95^2-5^2)\div10 ]^{0.5}

= [ ( 95 + 5 ) ( 95 − 5 ) ÷ 10 ] =\sqrt{[(95+5)(95-5)\div 10 ]}

= ( 9000 ÷ 10 ) = 30 = \sqrt{(9000\div 10 )}= \boxed{30}

6 Helpful 0 Interesting 0 Brilliant 0 Confused
Saarisht Thaman
Aug 27, 2015

just write 95^2 as (100-5)^2 and the rest happens itself

1 Helpful 0 Interesting 0 Brilliant 0 Confused
Uahbid Dey
Aug 26, 2015

√[(95² - 5²)/10] = √[(95+5)(95-5)/10] = √(100x90/10) = √9 x √100 = 3 x 10 = 30

1 Helpful 0 Interesting 0 Brilliant 0 Confused
Avik Saha
Aug 24, 2015

95=a; 5=b; a^2-b^2=(a+b)(a-b) so 95^2-5^2=(95+5)(95-5) =9000; square root of (9000/10)=30.

1 Helpful 0 Interesting 0 Brilliant 0 Confused
Mahdi Raza
Jun 7, 2020

\[\begin{align} &= \sqrt{\dfrac{95^2 - 5^2}{10}} \\ &= \sqrt{\dfrac{(95+5)(95-5)}{10}} \\ &= \sqrt{\dfrac{(100)(90)}{10}} \\ &= \sqrt{900} \\ &= \boxed{30}

\end{align}\]

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