## ML Aggarwal Class 8 Solutions for ICSE Maths Model Question Paper 1

**Choose the correct answer from the given four options (1-2):**

Question 1.

Sum of rational number \(\frac { 5 }{ 7 }\) and its additiveinverse is

(a) 1

(b) 0

(c) -1

(d) none of these

Solution:

Sum of \(\frac { 5 }{ 7 }\) and its additive inverse.

Question 2.

Product of two rational numbers is 1. If oneof them is \(\frac { 4 }{ 5 }\), then other is

Solution:

Product of two rational numbers = 1

One number = \(\frac { 4 }{ 5 }\), then second number

Question 3.

Find the value of x for which \(\left(\frac{4}{9}\right)^{x} \times\left(\frac{3}{2}\right)^{-1}\) = \(\frac{8}{27}\).

Solution:

Comparing, we get

2x + 1 = 3

⇒ 2x = 3 – 1 = 2

⇒ x = \(\frac{2}{2}\)

∴ x = 1

Question 4.

Express the following numbers in standard form:

(i) 0.0000000000578

(ii) 345700000000000

Solution:

(i) 0.0000000000578 = 5.78 × 10^{-11}

(ii) 345700000000000 = 3.457 × 10^{14}

Question 5.

Insert ten rational numbers between \(\frac{-4}{5}\) and \(\frac{2}{3}\).

Solution:

Ten rational numbers between \(\frac{-4}{5}\) and \(\frac{2}{3}\)

LCMof 5, 3 = 15

We take any 10 rational numbers among these.

Question 6.

Find the cube root of 50653.

Solution:

Cube root of 50653

Question 7.

Find the smallest number by which 3645 should be divided so that quotient is a perfect cube.

Solution:

3645

Factorising it we get

3645 = 3 × 3 × 3 × 3 × 3 × 3 × 5

Grouping the same kind of factors in 3’s,

we find that one factor 5 is left ungrouped.

So, dividing 3645 by 5, we get 729 which is a perfect cube

and its cube root is 3 × 3 = 9

Question 8.

If p = \(\frac{-3}{5}\), q = \(\frac{1}{2}\), r= \(\frac{-7}{9}\),then verify p × (q + r) = p × q + p × r.

Solution:

Hence proved L.H.S. = R.H.S.

Question 9.

Find the square root of 7056 by prime factorisation method.

Solution:

Square root of 7056 = \(\sqrt{7056}\)

Question 10.

Find the least number which must be added to 59000 to make it a perfect square.

Solution:

59000

Taking the square root of 59000 by division method we find that

(242)^{2} < 59000 < (243)^{2}

By adding 1449 – 1400 = 49

We shall get a perfect square 59049 and its square root = 243