Question

evaluate \[\huge \sqrt{ \frac{0.81 \times 10^{-5}}{2.25 \times 10^{7}}} \]

Answer 1

sorry i can't see

Answer 2

Hint: \( 0.9^2 = 0.81 \) and \( 1.5^2 = 2.25 \).

Answer 3

tomas

Answer 4

and 10^(-5)/(10^7) = 10^(-12)

Answer 5

Divide 0.81 by 2.25 so you get 0.36
0.36x10^-7x10^-5
0.36x10^-12
take full square root using calculator:
you get 6x10^-7 which is the answer.

Answer 6

well i'm not supposed to use a calculator so how do i use my head to arrive at 0.36... it seems possible but not easy -_-

Answer 7

Use the hint I wrote above. Then your expression is equal to
\[ \sqrt{ \frac{ 0.9^2}{1.5^2} \times 10^{-12} } \]
\[ = \frac{9}{15} \times 10^{-6} \]
\[ = \frac{3}{5} \times 10^{-6} \]
\[ = 0.6 \times 10^{-6} \]
\[ = 6 \times 10^{-7} \]

Answer 8

@Saso-Take 0.81 as 81 and 2.25 as 225 then use long division method.

Answer 9

the hard part is probably seeing that
\[\sqrt{.81}=.9\]
this is because
\[.9^2=.81\] but also because
\[.91=\frac{81}{100}\] so
\[\sqrt{.81}=\sqrt{\frac{81}{100}}=\frac{9}{10}=.9\]