Squares and Square Roots Test

Result

Squares and Square Roots Test - 14

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Weekly Quiz Competition

Question 1
1 / -0

By splitting into prime factors, find the square root of $$5184$$.

A
$$72$$

B
$$42$$

C
$$52$$

D
$$48$$

Solution

Prime factorisation of $$5184$$ can be obtained as,
$$ 5184 =2\times2\times2\times2\times2\times2\times3\times3\times3\times3$$
$$= {2} ^{6} \times { 3 } ^ {4} $$
$$\therefore \sqrt {5184} = \sqrt {{2} ^{6} \times { 3 } ^ {4}} = {2} ^{3} \times { 3 } ^ {2} = 8 \times 9 = 72 $$
Question 2
1 / -0

Find the smallest number by which 2592 be multiplied so that the product is a perfect square.

A
2

B
4

C
5

D
8

Solution

$$\textbf{Step-1: Find the prime factorization of given expression & ungrouped pair.}$$
$$\text{We have given 2592}$$
$$\therefore$$ $$\text{Prime factorization of}$$ $$2592 = 2 \times 2 \times 2 \times 2 \times 2 \times 3 \times 3 \times 3 \times 3$$
$$\text{Now,}$$
$$\text{On grouping the factors in pairs, we notice that one 2 is left out.}$$
$$\text{So, we should multiply 2592 with 2, so that prime factor 2 gets grouped in pairs.}$$
$$\textbf{Hence, 2592 should be multiplied by 2 to make it a perfect square.}$$ $$\textbf{Option - A}$$
Question 3
1 / -0

By splitting into prime factors, find the square root of $$396900$$

A
$$630$$

B
$$450$$

C
$$520$$

D
$$620$$

Solution

Prime factorisation of $$ 396900 = {2} ^{2} \times { 3 } ^ {4} \times { 5 } ^ {2} \times {7} ^ {2} $$
$$ \sqrt {396900} = \sqrt {{2} ^{2} \times { 3 } ^ {4} \times { 5 } ^ {2} \times {7} ^ {2} } = 2 \times {3}^{2} \times 5 \times 7= 630 $$.
Question 4
1 / -0

Find the square root of $$324$$.

A
$$18$$

B
$$16$$

C
$$28$$

D
$$24$$

Solution

The prime factorization of 324 is given as
$$324 = 2 \times 2 \times 3 \times 3 \times 3 \times 3$$
$$\sqrt{324} = \sqrt{\left(2\times2 \right) \times \left(3\times3 \right) \times \left(3\times 3\right)}= 2 \times 3 \times 3 = 18$$
$$\therefore \sqrt{324} = 18$$.
Question 5
1 / -0

Find the square root of $$4761$$.

A
$$69$$

B
$$59$$

C
$$49$$

D
$$48$$

Solution

$$\therefore \sqrt{4761} = 69$$

or,
Since the sum of digits of the given number is 18, therefore it is divisible by 3.
$$\Rightarrow 4761 = 3\times 1587 = 3\times 3\times 529 = 3\times 3\times 23\times 23 = $$ square of $$23$$
Question 6
1 / -0

The square root of $$15129$$ is

A
$$123$$

B
$$223$$

C
$$113$$

D
$$213$$

Solution

$$\therefore \sqrt{15129} = 123$$
Question 7
1 / -0

The square root of $$34969$$ is:

A
$$177$$

B
$$187$$

C
$$197$$

D
$$157$$

Solution

$$\therefore \sqrt{34969} = 187$$
or
$$34969=11\times 11\times 17\times 17$$
$$\sqrt{34969}=\sqrt{11\times 11\times 17\times 17}$$
$$=11\times 17=187$$
Question 8
1 / -0

Find the square root of $$1156$$.

A
$$34$$

B
$$54$$

C
$$61$$

D
$$21$$

Solution

So, the square root of $$1156$$ is $$34$$.
Question 9
1 / -0

The square root of $$69696$$ is

A
$$264$$

B
$$254$$

C
$$214$$

D
$$224$$

Solution

$$\therefore \sqrt {69696}=264$$
Question 10
1 / -0

The square root of $$7744$$ is

A
$$88$$

B
$$48$$

C
$$98$$

D
$$84$$

Solution

$$\therefore \sqrt{7714} = 88$$