Exploring Perfect Squares and Roots

What does 12 x 12 = 144 tell you about the square root?

• 16

Answer explanation

The equation 12 x 12 = 144 shows that 144 is a perfect square. Therefore, the square root of 144 is 12, which is represented as \(\sqrt{144} = 12\). This confirms the correct answer.

Tags

ONTARIO.MATH.7.B1.2

Which of the following numbers is a perfect square?

• 50

• 64

• 75

• 90

Answer explanation

A perfect square is an integer that is the square of another integer. Among the choices, 64 is 8 squared (8 x 8), while 50, 75, and 90 are not perfect squares.

Tags

ONTARIO.MATH.7.B1.2

Express 5,000,000 in expanded form using powers of ten.

Answer explanation

5,000,000 can be expressed as 5 multiplied by 1,000,000. Since 1,000,000 is 10 raised to the power of 6, the expanded form is 5 × 10^6, making this the correct choice.

Tags

ONTARIO.MATH.7.B1.1

Which of the following represents the number 1,234,567 in expanded form (using powers of 10)?

Answer explanation

The correct expanded form for 1,234,567 is 1 × 10^6 + 2 × 10^5 + 3 × 10^4 + 4 × 10^3 + 5 × 10^2 + 6 × 10^1 + 7 × 10^0, which represents each digit's value based on its position.

Tags

ONTARIO.MATH.7.B1.1

What is the square root of 225?

• 13

• 14

• 15

• 16

Answer explanation

The square root of 225 is the number that, when multiplied by itself, equals 225. Since 15 x 15 = 225, the correct answer is 15.

Tags

ONTARIO.MATH.7.B1.2

Which of the following numbers is not a perfect square?

• 81

• 100

• 121

• 130

Answer explanation

A perfect square is an integer that is the square of another integer. 81 (9x9), 100 (10x10), and 121 (11x11) are perfect squares, while 130 cannot be expressed as the square of an integer, making it the correct answer.

Tags

ONTARIO.MATH.7.B1.2

Which of the following is the expanded form of 700,000,000?

Answer explanation

The number 700,000,000 can be expressed in scientific notation as 7 times 10 raised to the power of 8, which is written as 7 \times 10^8. Therefore, the correct choice is 7 \times 10^8.

Tags

ONTARIO.MATH.7.B1.1

• 5

• 6

• 7

• 8

Answer explanation

To solve for x in the equation x^2 = 49, take the square root of both sides. This gives x = ±7. Since we are looking for the value of x, the correct answer is 7.

Tags

ONTARIO.MATH.7.B1.2

Which of the following multiplication sentences represents the square root of 81?

Answer explanation

The square root of 81 is 9, since 9 multiplied by 9 equals 81. Therefore, the correct multiplication sentence is 9 \times 9 = 81.

Tags

ONTARIO.MATH.7.B1.2

What does this picture tell you about the square root of 144?

(a)  

• The square root of 144 is 12.

• The square root of 144 is 14.

• The square root of 144 is 10.

• It doesn't tell me about the square root.

Answer explanation

The picture likely shows the number 144, and since the square root of 144 is 12, this confirms that the correct answer is 'The square root of 144 is 12.' The other options are incorrect.

Tags

CCSS.8.NS.A.1