Question

1 point
2.Which of the following is not a
perfect square ?
O a) 612
O b) 256
O c) 900
d) 144

Answer 1

Question

Which of the following is not a perfect square?

a) 612

b) 256

c) 900

d) 144

Answer

Let's take the 4 numbers one by one and try to find the square root of each of them.

We'll use the prime factorization method.

a) 612

$\begin{array}{c|c} \tt 2 & \sf{612 } \\ \cline{1-2} \tt 2 & \sf { 306} \\ \cline{1-2} \tt 3 & \sf{ 153 } \\ \cline{1-2} \tt 3& \sf{51 } \\ \cline{1-2} \tt & \sf{ 17}\\ \end{array}$

612 ⇒ 2 × 2 × 3 × 3 × 17

Pair the prime factors.

612 = (2 × 2) × (3 × 3) × 17

∴ 17 doesn't have a pair.

∴ 612 is not a perfect square.

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b) 256

$\begin{array}{c|c} \tt 2 & \sf{256 } \\ \cline{1-2} \tt 2 & \sf { 128} \\ \cline{1-2} \tt 2 & \sf{ 64 } \\ \cline{1-2} \tt 2& \sf{32 } \\ \cline{1-2} \tt 2 & \sf{ 16}\\ \cline{1-2} \tt 2 & \sf{8} \\ \cline{1-2} \tt 2 & \sf{4} \\ \cline{1-2} \tt & \sf{2}\\ \end{array}$

256 ⇒ 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2

Pair the prime factors.

256 = (2 × 2) × (2 × 2) × (2 × 2) × (2 × 2)

∴ All prime factors have a pair.

∴ 256 is a perfect square.

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c) 900

$\begin{array}{c|c} \tt 2 & \sf{900 } \\ \cline{1-2} \tt 2 & \sf { 450} \\ \cline{1-2} \tt 3 & \sf{ 225 } \\ \cline{1-2} \tt 3& \sf{75 } \\ \cline{1-2} \tt 5 & \sf{ 25}\\ \cline{1-2} \tt & \sf{5} \\ \end{array}$

900 ⇒ 2 × 2 × 3 × 3 × 5 × 5

Pair the prime factors.

900 = (2 × 2) × (3 × 3) × (5 × 5)

∴ All prime factors have a pair.

∴ 900 is a perfect square.

_______________________________

d) 144

$\begin{array}{c|c} \tt 2 & \sf{144 } \\ \cline{1-2} \tt 2 & \sf { 72} \\ \cline{1-2} \tt 2 & \sf{ 36 } \\ \cline{1-2} \tt 2& \sf{18 } \\ \cline{1-2} \tt 3 & \sf{ 9}\\ \cline{1-2} \tt & \sf{3} \\ \end{array}$

144 ⇒ 2 × 2 × 2 × 2 × 3 × 3

Pair the prime factors.

144 = (2 × 2) × (2 × 2) × (3 × 3)

∴ All prime factors have a pair.

∴ 144 is a perfect square.

∴ a) 612 is not a perfect square.

_______________________________

Answer 2

Answer:

Question

Which of the following is not a perfect square?

a) 612

b) 256

c) 900

d) 144

Answer

Let's take the 4 numbers one by one and try to find the square root of each of them.

We'll use the prime factorization method.

a) 612

$\begin{array}{c|c} \tt 2 & \sf{612 } \\ \cline{1-2} \tt 2 & \sf { 306} \\ \cline{1-2} \tt 3 & \sf{ 153 } \\ \cline{1-2} \tt 3& \sf{51 } \\ \cline{1-2} \tt & \sf{ 17}\\ \end{array}$

612 ⇒ 2 × 2 × 3 × 3 × 17

Pair the prime factors.

612 = (2 × 2) × (3 × 3) × 17

∴ 17 doesn't have a pair.

∴ 612 is not a perfect square.

_______________________________

b) 256

$\begin{array}{c|c} \tt 2 & \sf{256 } \\ \cline{1-2} \tt 2 & \sf { 128} \\ \cline{1-2} \tt 2 & \sf{ 64 } \\ \cline{1-2} \tt 2& \sf{32 } \\ \cline{1-2} \tt 2 & \sf{ 16}\\ \cline{1-2} \tt 2 & \sf{8} \\ \cline{1-2} \tt 2 & \sf{4} \\ \cline{1-2} \tt & \sf{2}\\ \end{array}$

256 ⇒ 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2

Pair the prime factors.

256 = (2 × 2) × (2 × 2) × (2 × 2) × (2 × 2)

∴ All prime factors have a pair.

∴ 256 is a perfect square.

_______________________________

c) 900

$\begin{array}{c|c} \tt 2 & \sf{900 } \\ \cline{1-2} \tt 2 & \sf { 450} \\ \cline{1-2} \tt 3 & \sf{ 225 } \\ \cline{1-2} \tt 3& \sf{75 } \\ \cline{1-2} \tt 5 & \sf{ 25}\\ \cline{1-2} \tt & \sf{5} \\ \end{array}$

900 ⇒ 2 × 2 × 3 × 3 × 5 × 5

Pair the prime factors.

900 = (2 × 2) × (3 × 3) × (5 × 5)

∴ All prime factors have a pair.

∴ 900 is a perfect square.

_________________________