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