Finding Square of a Number Using Identity

Q.

Rationalize the denominators of $\frac{1}{\sqrt{7}-2}$

Q.

Rationalize the denominators of $\frac{1}{\sqrt{5}+\sqrt{2}}$

Q.

Rationalize the denominators of $\frac{1}{\sqrt{7}-\sqrt{6}}$

Q.

Find the digits A and B. [3 MARKS]

$\begin{array}{c}BA\\ \times B3\\ 57A\end{array}$

Q. If $x+\frac{1}{x}=3$, then what is the value of $x^8+\frac{1}{x^8}?$

1. 2207
2. 1097
3. 3407
4. 47

Q.

Using the formula $(a+b{)}^2=(a^2+2ab+b^2$, evaluate:
(i) $(310{)}^2$
(ii) $(508{)}^2$
(iii) $(630{)}^2$

Q.

Find the square of $85$.

Q.

Find the squares of the following numbers using the identity $a+b{)}^2=a^2+2ab+b^2$

(i) 405 (ii) 510
(iii) 1001 (iv) 209
(v) 605

Q.

Evaluate:
(i) $(38{)}^2-(37{)}^2$
(ii) $(75{)}^2-(74{)}^2$
(iii) $(92{)}^2-(91{)}^2$
(iv) $(105{)}^2-(104{)}^2$
(v) $(141{)}^2-(140{)}^2$
(vi) $(218{)}^2-(217{)}^2$

Q.

Question 1 (v)
Find the squares of the following numbers:

71

Q.

Question 1 (ii)
Find the squares of the following numbers:

35

Q.

Find the squares of the following numbers by visual method:
(i) 52 (ii) 95
(iii) 505 (iv) 702
(v) 99

Q.

Find the square of the following numbers: $46$

Q.

Question 1 (vi)
Find the squares of the following numbers:

46

Q.

Find the squares of the following numbers :
(i) 127 (ii) 503
(iii) 451 (iv) 862
(v) 265

Q.

Question 1 (iii)
Find the squares of the following numbers:

86

Q.

Question 93

Solve the following question:

Using distributive law, find the squares of
a) 101
b) 72

Q.

Use the short cut method to find $(97{)}^2$.

1. 6439

2. 9709

3. 9409

4. 9439

Q.

$398=964,118=164,356=936,423=?$

What comes in place of $?$

Q.

Using the formula $(a-b{)}^2=(a^2-2ab+b^2),$ Evaluate:
(i) $(196{)}^2$
(ii) $(689{)}^2$
(iii) $(891{)}^2$

Q. $\text{Evaluate:}{37}^2-{36}^2.$

Q.

Evaluate :

(i) ${37}^2-{36}^2$ (ii) ${85}^2-{84}^2$

(iii) ${101}^2-{100}^2$

Q.

Find the square of 48.

1. 2284

2. 2304

3. 2464

4. 2364

Q.

Question 74

State whether the following statement is true or false:

A number having 7 at its one's place will have 3 at the unit's place of its square.

Q. Square of number 37 can be found in two steps.



What is a?

1. 50

2. 75

3. 25

4. 100

Q.

Question 27

Fill in the blanks to make the statements true.

The unit's digit in the square of 1294 is ___

Q.

Find the number of non square numbers between the square of 13 and 12. Also write the formula.

Q.

Find the square of 48.

1. 2284

2. 2304

3. 2464

4. 2364

Q.

Question 1 (i)
Find the squares of the following numbers:
32

Q. Square of number 37 can be found in two steps.



What is a?

1. 50

2. 75

3. 25

4. 100