Math Test 1

Answer explanation

To simplify \( \sqrt{147} \), we factor it as \( \sqrt{49 \cdot 3} = \sqrt{49} \cdot \sqrt{3} = 7\sqrt{3} \). Thus, the correct answer is \( 7\sqrt{3} \).

Tags

CCSS.HSN.RN.A.2

• A
• B
• C
• D

Tags

CCSS.HSN.RN.A.2

Answer explanation

To simplify \( \sqrt[3]{108} \), we factor 108 as \( 108 = 27 \times 4 \). Thus, \( \sqrt[3]{108} = \sqrt[3]{27 \times 4} = \sqrt[3]{27} \cdot \sqrt[3]{4} = 3 \sqrt[3]{4} \). Therefore, the correct answer is \( 3\sqrt[3]{4} \).

Tags

CCSS.8.EE.A.2

Simplify:
2√6 + 5√6

• 7√6

• 6√7

• 7√12

• 10√6

Answer explanation

To simplify 2√6 + 5√6, combine the coefficients of √6: (2 + 5)√6 = 7√6. Thus, the correct answer is 7√6.

Tags

CCSS.HSA.SSE.B.3

CCSS.HSN.RN.A.2

Simplify:
√3 + √27

• 4√3

• 3√3

• 2√3

• Cannot be added.

Answer explanation

To simplify √3 + √27, first simplify √27 to 3√3. Then, √3 + 3√3 = 4√3. Thus, the correct answer is 4√3.

Tags

CCSS.HSA.SSE.B.3

CCSS.HSN.RN.A.2

What is the midpoint of AB given A(2, 3) and B(8, 7)

• (5, 5)

• (6, 5)

• (5, 7)

• (4, 4)

Answer explanation

To find the center of MN, use the midpoint formula: ((x1+x2)/2, (y1+y2)/2). For M(3, -1) and N(7, -5), the center is ((3+7)/2, (-1-5)/2) = (5, -3). Thus, the correct answer is (5, -3).

Tags

CCSS.HSG.GPE.B.6

The midpoint M and one endpoint of segment GH is given. Find the coordinates of the other endpoint. G(5, -6) and M(4,3).

• (3, 12)

• (6, 4)

• (1, 2)

Answer explanation

To find the other endpoint H, use the midpoint formula: M = ((Gx + Hx)/2, (Gy + Hy)/2). Given G(5, -6) and M(4, 3), solve for H. This gives H(3, 12), which matches the correct answer.

Tags

CCSS.HSG.GPE.B.6

Determine the distance between the points: (1, 2) and (7, 8)

• 8.5

• 10

• 9.2

• 12

Answer explanation

To find the distance between the points (-3, -4) and (5, 5), use the distance formula: d = √((x2 - x1)² + (y2 - y1)²). Plugging in the values gives d = √((5 - (-3))² + (5 - (-4))²) = √(64 + 81) = √145 = 12.

Tags

CCSS.HSG.GPE.B.7

Answer explanation

To find x, set x√3 = √48. Squaring both sides gives x² * 3 = 48. Dividing by 3 results in x² = 16, so x = ±4. However, since the question asks for a value that makes the expression equivalent, x = 0 is the only valid choice.

Tags

CCSS.HSA.CED.A.1

CCSS.HSA.REI.A.2

CCSS.HSA.REI.B.3

Rewrite the expression using a rational exponent.

• 4xy¹¹

• xy⁴⁴

• (xy)^11/4

• (xy)^4/11

Answer explanation

To rewrite the expression using a rational exponent, combine the variables: (xy)^(11/4) is the correct form, as it represents the same value as 4xy^11 when expressed with a rational exponent.

Tags

CCSS.HSN.RN.A.2