Mathematics

Linear Equations in Two Variables

Question:

Rationalise the denominator of : 1 7 + 3 2

Answer:

We have,

1 7 + 3 2 = 1 7 + 3 2 × 7 - 3 2 7 - 3 2 = 7 - 3 2 (7)2 - 3 2 = 7 - 3 2 49 - 18 = 7 - 3 2 31

previuos
next

Linear Equations in Two Variables

Q 1.

Find the value to three places of decimals, of each of the following: It is given that 2 = 1.414 , 3 = 1.732, 10 = 3.162 and 5 = 2.236 (approx.)

(i) 1 2 (ii) 1 3 (iii) 1 10

Q 2.

Simplify:
(i) 5 + 2 2 [NCERT] (ii) 11 - 5 2

Q 3.

Rationalise the denominator in each of the following:

(i) 2 7 [NCERT] (ii) 2 3 3 (iii) 2 7 11

Q 4.

Simplify each of the following :

(i) 3 5 3 + 2 5 + 3 (ii) 4 + 5 4 5 + 4 5 4 + 5 (iii) 5 2 5 + 2 5 + 2 5 2

Q 5.

if a = 2 5 2 + 5 and b = 2 + 5 2 5 , find a2 b2

Q 6.

if x = 3 + 2 3 2 and y = 3 2 3 + 2 , find x2 + y2

Q 7.

Simplify:
(i) 5 + 5 5 - 5 (ii) 3 + 2 2 3 - 2 2

Q 8.

If both a and b are rational numbers, find the values of a and b in each of the following equalities :

(i) 3 1 3 + 1 = a + b 3 (ii) 3 + 7 3 7 = a + b 7 (iii) 5 + 2 3 7 + 4 3 = a + b 3

(iv) 5 + 3 7 4 3 = 47 a + 3 b (v) 5 + 3 5 3 = a + b 15 (vi) 2 + 3 3 2 2 3 = a b 6

Q 9.

Simplify each of the following by rationalising the denominator:

(i) 1 5 + 2 (ii) 5 + 6 5 - 6 (iii) 7 + 3 5 7 - 3 5 (iv) 2 3 5 2 3 + 3 3

Q 10.

Rationalise the denominator of :
2 3

Q 11.

Simplify each of the following by rationalising the denominator:

(i) 1 5 + 2 (ii) 5 + 6 5 - 6 (iii) 7 + 3 5 7 - 3 5 (iv) 2 3 5 2 3 + 3 3

Q 12.

Given that 5 = 2.236 approximately, find to three places of decimals the value of 2 5

Q 13.

if x = 1 2 3 , find the value of x 3 2x2 7x + 5

Q 14.

If x = 2 + 3 , find the value of x2 + 1 x2

Q 15.

Prove that :

= 1 3 8 1 8 7 + 1 7 6 1 6 5 + 1 5 2 = 5

Q 16.

Rationalise the denominator of : 1 3 + 2

Q 17.

Prove that :

1 1 + 2 + 1 2 + 3 + 1 3 + 4 + 1 4 + 5 + 1 5 + 6 + 1 6 + 7 + 1 7 + 8 + 1 8 + 9 = 2

Q 18.

If x = 3 - 2 2 , find the value of x2 + 1 x2

Q 19.

Rationalise the denominator of : 5 3 - 5

Q 20.

Rationalise the denominator of : 1 7 + 3 2

Q 21.

Simply the following expression:
(i) 3 + 3 2 + 2 [NCERT] (ii) 5 + 7 2 + 5

Q 22.

If 2 = 1.414 , find the value of 3 ÷ 6 upto three places of decimals.

Q 23.

If x = 1 2 , find the value of x 1 x 3

Q 24.

Simply each of the following: (i) 5 16 × 5 2 (ii) 4 243 4 3

Q 25.

Find the value to three places of decimals, of each of the following:
It is given that 2 = 1.414 , 3 = 1.732, 10 = 3.162 and 5 = 2.236 (approx.).
(i) 2 + 1 5 (ii) 2 - 3 3 (iii) 10 - 5 2

Q 26.

Evaluate 15 10 + 20 + 40 - 5 - 80 , is being given that 5 = 2.236 and 10 = 3.162