Name: Estimation of Square Roots
Uploaded: 2019-07-19
Duration: 6 min 2 s
Description: For not-perfect squares, we can estimate their square root to the closest whole number. Learn how to estimate the square root of non-perfect squares.

Question

Using prime factorization method, find which of the following numbers are perfect squares?

$189, 225, 2048, 343, 441, 2961, 11025, 3549$

Accepted Answer

Given numbers,

$189, 225, 2048, 343, 441, 2961, 11025, 3549$

$189$ prime factors are

$189 = 3 \times 3 \times 3 \times 7$
Since, it does not have a equal pair of factors $189$ is not a perfect square.

$225$ prime factors are

$225 = (5 \times 5) \times (3 \times 3)$
Since $225$ has a equal pair of factors.

$∴$ It is a perfect square.

$2048$ prime factors are

$2048 = (2 \times 2) \times (2 \times 2) \times (2 \times 2) \times (2 \times 2) \times (2 \times 2) \times 2$
Since it does not have equal pair of factors $2048$ is not a perfect square.

$343$ prime factors are

$343 = (7 \times 7) \times 7$
Since it does not have equal pair of factors is not a perfect square.

$441$ prime factors are

$441 = (7 \times 7) \times (3 \times 3)$
since $441$ has equal pair of factors.

$∴$ It is a perfect square.

$2961$ prime factors are

$2961 = (3 \times 3) \times (3 \times 3) \times (3 \times 3) \times (2 \times 2)$
Since $2961$ has equal pair of factors.

$∴$ It is a perfect square.

$11025$ prime factors are

$11025 = (3 \times 3) \times (5 \times 5) \times (7 \times 7)$
Since $11025$ has equal pair of factors.

$∴$ It is a perfect square.

$3549$ prime factors are

$3549 = (13 \times 13) \times 3 \times 7$

Since it does not have equal pair of factors $3549$ is not a perfect square.

Using prime factorization method, find which of the following numbers are perfect squares?

$189, 225, 2048, 343, 441, 2961, 11025, 3549$

Important Questions on Squares and Square Roots

Learn and Prepare for any exam you want !

Using prime factorization method, find which of the following numbers are perfect squares? 189, 225, 2048, 343, 441,2961,11025, 3549

Important Questions on Squares and Square Roots

Learn and Prepare for any exam you want !

Using prime factorization method, find which of the following numbers are perfect squares?

$189, 225, 2048, 343, 441, 2961, 11025, 3549$