Evaluate: 333 289 - Vidyadip

Question

Evaluate:
$\sqrt{3\frac{33}{289}}$

✓

Answer

$\sqrt{3\frac{33}{289}}$
$=\sqrt{\frac{3\times289+33}{289}}$
$=\sqrt{\frac{867+33}{289}}$
$=\sqrt{\frac{900}{289}}$
$\begin{array}{c|c}2&900\\\hline2&450\\\hline3&225\\\hline3&75\\\hline5&25\\\hline5&5\\\hline&1\end{array}$
$\begin{array}{c|c}17&289\\\hline17&17\\\hline&1\end{array}$
$=\sqrt{\frac{\overline{2\times2}\times\overline{3\times3}\times\overline{5\times5}}{17\times17}}$
$=\frac{2\times3\times5}{17}$
$=\frac{30}{17}$
$=1\frac{13}{17}$

Need a full question paper?

Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.

Start Generating Free

Explore more

More "3 Mark Question" from Squares and Square Roots→Squares and Square Roots — all question types→Maths STD 8 question papers→Maharashtra Board STD 8 question papers→Maharashtra Board question paper generator→

Similar questions

Robin purchased an old car for Rs. 73500. He spent Rs. 10300 on repairs and paid Rs. 2600 for its insurance. Then he sold it to a mechanic for Rs. 84240. What was his percentage gain or loss?

In a rational number, twice the numerator is 2 more than the denominator. If 3 is added to each, the numerator and the denominator, the new fraction is $\frac{2}{3}.$ Find the original number.

Find following product:
$\big(-\frac{1}{27}\text{a}^2\text{b}^2\big)\times\big(\frac{9}{2}\text{a}^3\text{b}^2\text{c}^2\big)$

A quadrilateral has three acute angles, each measuring 75°. Find the measure of the fourth angle.

Area of a parallelogram is 83.2 sq.cm. If its height is 6.4 cm, find the length of its base.

Length of the two parallel sides of a trapezium are 8.5 cm and 11.5 cm respectively and its height is 4.2 cm, find its area.

Find the amount of Rs. 2400 after 3 years, when the interest is compounded annually at the rate of 20% per annum.

The population of a town is 125000. It is increasing at the rate of 2% per annum. What will be its population after 3 years?

Find the value of $a$, if $x+2$ is a factor of $4 x^4+2 x^3-3 x^2+8 x+5 a$.

Find the greatest common factor of the polynomial:
$2 x^3 y^2, 10 x^2 y^3, 14 x y$