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Teachers & SchoolsACT Math: Intermediate Algebra Drill 2, Problem 3. Which of the following is equal to the expression shown?

ACT Math | Intermediate Algebra |

ACT Mathematics | Intermediate Algebra |

Algebra | Square Roots |

Foreign Language | Arabic Subtitled Chinese Subtitled Korean Subtitled Spanish Subtitled |

Intermediate Algebra | Radical and rational expressions Rational, radical, and logarithmic expressions |

Language | English Language |

Product Type | ACT Math |

So in this case - we want a perfect square that's in the form of (a +b) times (a - b)...

Since we have the square root of 3 plus the square root of 5 on the bottom...

we have to multiply the fraction

by root 3 minus root 5 times over root 3 minus root 5...which is the equivalent of 1.

Based on the perfect square formula... with a equaling root 3 and b equaling

root 5...we have the bottom of the fraction simplifying to 3 minus 5...or negative 2.

We can use simple distribution properties for the top of the fraction.

Root 3 times root 3 equals 3. Root 3 times negative root 5 equals negative root 15...negative

1 times root 3 equals negative root 3...and negative 1 times negative root 5 equals positive root 5.

All over NEGATIVE 2.

But looking at our answer choices...none of them have a negative 2 at the bottom.

So let's just move it to the top. Keep in mind that we have to take the negative of

the ENTIRE top of the fraction...so we have to distribute a negative to each number...

Negative 3 plus root 15 plus root 3 minus root 5--all over 2.

Looks like answer choice E is the right one.