Question
Evaluate the following: $\Big\{(6^2+8^2)^{\frac{1}{2}}\Big\}^3$
✓
Answer
To evaluate the value of the given expression, we can proceed as follows: $\Big\{(6^2+8^2)^{\frac{1}{2}}\Big\}^3$
$=\Big\{(36+64)^{\frac{1}{2}}\Big\}^3$
$=\Big\{(100)^{\frac{1}{2}}\Big\}^3$
$=\Big\{\sqrt{(100)}\Big\}^3$
$=\Big\{\sqrt{(10\times10)}\Big\}^3$
$=\{10\}^3$
$10\times10\times10=1000$
$=\Big\{(36+64)^{\frac{1}{2}}\Big\}^3$
$=\Big\{(100)^{\frac{1}{2}}\Big\}^3$
$=\Big\{\sqrt{(100)}\Big\}^3$
$=\Big\{\sqrt{(10\times10)}\Big\}^3$
$=\{10\}^3$
$10\times10\times10=1000$
Need a full question paper?
Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.
Explore more
Similar questions
Multiply: $\big(\frac{\text{x}}{7}+\frac{\text{x}^2}{2}) \ \text{by}\big(\frac{2}{5}+\frac{9\text{x}}{4}\big)$
→Campus and Welfare Committee of school is planning to develop a blue shade for painting the entire school building. For this purpose various shades are tried by mixing containers of blue paint and white paint. In each of the following mixtures, decide which is a lighter shade of blue and also find the lightest blue shade among all of them.
If one container has one litre paint and the building requires $105$ litres for painting, how many container of each type is required to paint the building by darkest blue shade?
→If one container has one litre paint and the building requires $105$ litres for painting, how many container of each type is required to paint the building by darkest blue shade?
Solve the linear equation $x + 7 - \frac{{8x}}{3} = \frac{{17}}{6} - \frac{{5x}}{2}$
→If a property holds for rational number, will it also hold for integers? For whole numbers? Which will? Which will not?
Find the square root of the following correct to three places of decimal: $5$
→A mason has made a concrete slap. He needs it to be rectangular. In what different ways can he make sure that it is a rectangular?
Find the value of x for which $\Big(\frac{5}{3}\Big)^{-4}\times\Big(\frac{5}{3}\Big)^{-5}=\Big(\frac{5}{3}\Big)^{3\text{x}}$
→The curved surface area of a cylinder is $2\pi(\text{y}^2-7\text{y}+12)$ and its radius is $(y - 3)$. Find the height of the cylinder $(C.S.A$. of cylinder = $2\pi\text{rh}$).
→Top surface of a table is trapezium in shape. Find its area if its parallel sides are $1\ m$ and $1.2\ m$ and perpendicular distance between them is $0.8\ m.$
→Factorise the expressions: $q^2- 10q + 21$
→