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16 votes
16 votes
Which choices are equivalent to the expression below? Check all that apply.

5√3
A. √45
B. 15-√5
C. 75
D. √76
E. √√√√5
F. √25-√3

Which choices are equivalent to the expression below? Check all that apply. 5√3 A-example-1
User Zerefel
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1 Answer

26 votes
26 votes

Answer:

Options: B, C, and F

Explanation:

5√3 = 8.660254

√45 (Not equivalent)

⇒ √3*3*5 ⇒ Rewrite 45 as its prime factors

⇒ √(3*3)*5 ⇒ Group the same prime factors into pairs.

⇒ √3²*5 ⇒ Rewrite each pair in exponent form.

⇒ 3√5 ⇒ Use this rule: √x² = x

Decimal Form: 6.708204

√15 · √5 (Equivalent)

⇒ √75 ⇒ Simplify

⇒ 5√3 ⇒ Simplify √75 to 5√3

Decimal Form: 8.660254

75 (not equivalent)

1: Whole number, not a decimal.

√75 (Equivalent)

⇒ Rewrite 75 as its prime factors

√3*5*5

⇒ Group the same prime factors into pairs.

√(5*5)*3

⇒ Rewrite each pair in exponent form.

√5²*3

⇒ Use this rule: √x² = x

5√3

Decimal Form: 8.660254

√3 · √ 5 (Not equivalent)

⇒ √15 ⇒ Simplify

Decimal Form: 3.872983

√25 · √3 (Equivalent)

1) Since 5 × 5 = 25, the square root of 25 is 5.

⇒ 5 √ 3

Decimal Form: 8.660254

User Svetoslav Petkov
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3.2k points