Writing a Number as a Product of Its Primes (Power Rotation)

Q.

Find the square root of the following decimal number:
7.29

1. 1.2

2. 2

3. 2.7

4. 2.3

Q. What is the smallest number by which 648 must be multiplied so that the product becomes a perfect square?

1. 3
2. 5
3. 7
4. 2

Q. 8820 $÷$ ____ is a perfect square.

1. 3
2. 5
3. 2
4. 7

Q.

1.44 is the perfect square of 1.2

1. False

2. True

Q. Express$16,200$ as a product of powers of prime numbers.

1. $2^3\times 3^3\times 5^4$
2. $2^3\times 3^4\times 5^2$
3. $2^4\times 3^3\times 5^3$
4. $2^3\times 3^3\times 5^3$

Q.

Show that $500$ is not a perfect square.

Q. Find the square root of 1024.

Q. Express 16, 200 as a product of powers of prime numbers in the exponential form.

1. $2^3\times 3^3\times 5^4$
2. $2^4\times 3^3\times 5^3$
3. $2^3\times 3^3\times 5^3$
4. $2^3\times 3^4\times 5^2$

Q.

The square root of 22500 is equal to

1. $150$

2. $250$

3. $450$

4. $350$

Q.

Which of the following correctly represents the 882 as the product of its prime power.

1. $2^2\times 3^2\times 7$

2. $2^2\times 3\times 7^2$

3. $2^2\times 3^2\times 7^2$

4. $2\times 3^2\times 7^2$

Q.

Express 32000 as a product of powers of prime factors

1. 2⁸ x 5²

2. 2⁸ x 5³

3. 2⁷ x 5⁴

4. 2⁸ x 54³

Q.

Which of the following correctly represent 588 as the product of its prime power.

1. $2\times 3^2\times 7^2$

2. $2^2\times 3\times 7^2$

3. $2^2\times 3^2\times 7^2$

4. $2^2\times 3^2\times 7$

Q.

Which of the following correctly represents 720 as the product of its prime power.

1. $2^4\times 3^2\times 5^2$

2. $2^2\times 3^4\times 5^2$

3. $2^4\times 3^2\times 5$

4. $2^2\times 3^2\times 5^2$

Q.

Which of the following correctly represents the 676 as the product of its prime power.

1. $2^2\times 3^4$

2. $3^4\times 13$

3. $2^2\times {13}^2$

4. $2^2\times 3^1\times {13}^2$

Q. The approximate value of the square root of 285 = .

1. 15
2. 16
3. 17
4. 18

Q.

Which of the following correctly represents 98 as the product of its prime power.

1. $2^2\times 7$

2. $2^2\times 7^2$

3. $2\times 7^2$

4. $2\times 7$

Q. Which of the following correctly represents 450 as the product of its prime power.

1. $2^2$ x $3^2$ x $5$
2. 2 x $3^2$ x $5^2$
3. $2^2$ x $3$ x $5^2$
4. $2^2$ x $3^2$ x $5^2$

Q.

Which of the following correctly represent 294 as the product of its prime power?

1. $294=2\times 3^2\times 7^2$

2. $294=2^2\times 3\times 7^2$

3. $294=2^2\times 3^2\times 7^2$

4. $294=2\times 3\times 7^2$

Q.

Which of the following correctly represents 294 as the product of its prime power?

1. $294=2\times 3^2\times 7$

2. $294=2^{\times }3\times 7$

3. $294=2^{\times }3\times 7^2$

4. $294=2\times 3\times 7^2$

Q.

Which of the following correctly represents the 450 as the product of its prime power.

1. $2^2\times 3^2\times 5$

2. $2\times 3^2\times 5^2$

3. $2^2\times 3\times 5^2$

4. $2^2\times 3^2\times 5^2$

Q.

What is the smallest number by which 2592 must be multiplied so that the product is a perfect square?

1. 5

2. 3

3. 2

4. 7

Q.

If using prime factorization method, we get $\sqrt{\left(2025\right)}=3^2\times k$, then the value of $k$ is equal to:

1. 45
2. 3
3. 9
4. 5