Finding Square Root by Long Division Method

Q.

Find the largest number of 3 digits which is a perfect square.

Q. The area of a square field is 60025 $m^2$. A man cycles along its boundary at 18 km/hr. In how much time will he return to the starting point?

Q. Find the least number which must be added to 6203 to obtain a perfect square. Find this perfect square and its square root.

Q.

Find the least number of six-digits which is a perfect square.

Q.

Find the least number which must be added to the following numbers to make them a perfect square :

(i) 5607 (ii) 4931 (iii) 4515600 (iv) 37460 (v) 506900

Q.

Find the value of $sqrt5$ correct to 2 decimal places; then use it to find the square root of $\frac{3-\sqrt{5}}{3+\sqrt{5}}$ correct to 2 significant digits.

Q.

Question 1 (vii)
Find the square roots of each of the following numbers by Division method:

7921

Q. Evaluate: $\sqrt{3}$ up to two places of decimal.

Q.

Find the square root of 7.832 correct to :

(i) 2 decimal places

(ii) 2 significant digits.

Q.

Find the least number which must be subtracted from $7581$ to obtain a perfect square. Find this perfect square and its square root.

Q.

Evaluate $\sqrt{0.9}$ correct up to two places of decimal.

Q.

A general arranges his soldiers in rows to form a a perfect square.He finds that in doing so, 60 soldiers are left out.IF the total number of soldiers be 8160, find the number of soldiers in each row.

Q. Find the least number which must be added to 8400 to obtain a perfect square. Find this perfect square and its square root.

Q.

Find the square root of :

(i) 245 correct to two places of decimal.

(ii) 496 correct to three places of decimal.

(iii) 82.6 correct to two places of decimal.

(iv) 0.065 correct to three places of decimal.

(v) 5.2005 correct to two places of decimal.

(vi) 0.602 correct to two places of decimal.

Q. Find the least number of four digits which is a perfect square. Also find the square root of the number so obtained.

Q.

Find the square root of :

(i) $\frac{1764}{2809}$ (ii) $\frac{507}{4107}$

(iii) $\sqrt{108\times 2028}$ (iv) $0.01+\sqrt{0.0064}$

Q.

Find the least number that must be added to 1300 so as to get a perfect square.

1. 67

2. 71

3. 68

4. 69

Q. Find the length of each side of a square whose area is equal to the area of a rectangle of length 13.6 metres and breadth 3.4 metres.

Q.

Question 9.
There are 500 children in a school. For a P.T. drill, they have to stand in such a manner that the number of rows is equal to number of columns. How many children would be left out in this arrangement?

Q.

For each of the following, find the least number that must be subtracted so that the resulting number is a perfect square.
(i) 796 (ii) 1886 (iii) 23497

Q.

Find the smallest number which must be added to 2300 so that it becomes a perfect square.

Q.

Question 1 (iii)
Find the square roots of each of the following numbers by Division method:

3481

Q.

Find the square root of each of the following correct to two decimal places :

(i) $3\frac{4}{5}$ (ii) $6\frac{7}{8}$

Q. Find the square root of 363609 [3 MARKS]

Q.

Question 1 (ii)
Find the square roots of each of the following numbers by Division method:

4489

Q.

Find the square root of 3364 by Long division Method.

1. 58
2. 68
3. 78
4. 88

Q.

What is the relationship between two pairs ?

$121:12::25:?$

Q. Evaluate: $\sqrt{92416}$

Q.

Find the square root of 7 correct to two decimal places; then use it to find the value of

$\sqrt{\frac{4+\sqrt{7}}{4+\sqrt{7}}}$ correct to three significant digits.

Q. Evaluate: $\sqrt{10404}$