Review From the following which square number is divisible by 6 9 15 a 90 b 180 c 720 d 900

Mẹo Hướng dẫn From the following which square number is divisible by 6 9 15 a 90 b 180 c 720 d 900 2022

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Solution:

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For each of the following numbers, find the smallest whole number by which it should be multiplied so as to get a perfect square number. Also find the square root of the square number so obtained. (i) 252 (ii) 180 (iii) 1008 (iv) 2028 (v) 1458 (vi) 768Which square number is divisible by each of the numbers 6 9 15?What is the least perfect square exactly divisible by each of the number 6 9 15 and 20?What is the smallest square number divided by 6 9 and 10?What is the smallest square number divisible by 2456 and 9?

We have to find the smallest whole number by which the number should be multiplied so as to get a perfect square number

To get a perfect square, each factor of the given number must be paired.

(i) 252

From the following which square number is divisible by 6 9 15 a 90 b 180 c 720 d 900

Hence, prime factor 7 does not have its pair. If 7 gets a pair, then the number becomes a perfect square. Therefore, 252 has to be multiplied by 7 to get a perfect square.

So, perfect square is 252 × 7 = 1764

1764 = 2 × 2 × 3 × 3 × 7 × 7

Thus, √1764 = 2 × 3 × 7 = 42

(ii) 180

Hence, prime factor 5 does not have its pair. If 5 gets a pair, then the number becomes a perfect square. Therefore, 180 has to be multiplied by 5 to get a perfect square.

So, perfect square is 180 × 5 = 900

900 = 2 × 2 × 3 × 3 × 5 × 5

Thus, √900 = 2 × 3 × 5 = 30

(iii) 1008

Hence, prime factor 7 does not have its pair. If 7 gets a pair, then the number becomes a perfect square. Therefore, 1008 has to be multiplied by 7 to get a perfect square.

So, perfect square is 1008 × 7 = 7056

7056 = 2 × 2 × 2 × 2 × 3 × 3 × 7 × 7

Thus, √7056 = 2 × 2 × 3 × 7 = 84

(iv) 2028

Hence, prime factor 3 does not have its pair. If 3 gets a pair, then the number becomes a perfect square. Therefore, 2028 has to be multiplied by 3 to get a perfect square.

So, perfect square is 2028 × 3 = 6084

6084 = 2 × 2 × 13 × 13 × 3 × 3

Thus, √6084 = 2 × 13 × 3 = 78

(v) 1458

Hence, prime factor 2 does not have its pair. If 2 gets a pair, then the number becomes a perfect square. Therefore, 1458 has to be multiplied by 2 to get a perfect square.

So, perfect square is 1458 × 2 = 2916

2916 = 3 × 3 × 3 × 3 × 3 × 3 × 2 × 2

Thus, √2916 = 3 × 3 × 3 × 2 = 54

(vi) 768

Hence, prime factor 3 does not have its pair. If 3 gets a pair, then the number becomes a perfect square. Therefore, 768 has to be multiplied by 3 to get a perfect square.

So, perfect square is 768 × 3 = 2304

2304 = 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 3 × 3

Thus, √2304 = 2 × 2 × 2 × 2 × 3 = 48

☛ Check: NCERT Solutions for Class 8 Maths Chapter 6

Video Solution:

For each of the following numbers, find the smallest whole number by which it should be multiplied so as to get a perfect square number. Also find the square root of the square number so obtained. (i) 252 (ii) 180 (iii) 1008 (iv) 2028 (v) 1458 (vi) 768

[embed]https://www.youtube.com/watch?v=hcwcxEsMG1o[/embed]

NCERT Solutions for Class 8 Maths Chapter 6 Exercise 6.3 Question 5

Summary:

For each of the following numbers, (i) 252 (ii) 180 (iii) 1008 (iv) 2028 (v) 1458 (vi) 768 the smallest whole number by which it should be multiplied so as to get a perfect square number and the square root of the square number so obtained are as follows: (i) 7; √1764 = 42 (ii) 5; √900 = 30 (iii) 7; √7056 = 84 (iv) 3; √6084 = 78 (v) 2; √2916 = 54 and (vi) 3; √2304 = 48

☛ Related Questions:

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Which square number is divisible by each of the numbers 6 9 15?

i.e. each prime factor should be in square. So, the smallest square number that can be divided by 6, 9 and 15 is 900.

What is the least perfect square exactly divisible by each of the number 6 9 15 and 20?

Hence least square number divisible by 6,9,15 and 20 is 900.

What is the smallest square number divided by 6 9 and 10?

Hence, the answer is 3600.

What is the smallest square number divisible by 2456 and 9?

The correct answer is 900, which is the least common square multiple of 2, 4, 5, 6, and 9. 900 is the square of 30. For divisibility: 900/2 = 450. Tải thêm tài liệu liên quan đến nội dung bài viết From the following which square number is divisible by 6 9 15 a 90 b 180 c 720 d 900