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Teachers & SchoolsMathematical Reasoning Drill 3 Problem 1. Which of the following is the best estimate of [3.05(7.95) - 4]^{2}?

Algebra | Systems of Equations |

CAHSEE Math | Mathematical Reasoning |

Language | English Language |

Mathematical Reasoning | Estimation |

So, we don’t have to multiply 3.05 by 7.95…

…we just have to find something close to that product.

To do that, we can use rounding.

Turns out, 3.05 is pretty close to 3, and 7.95 is pretty close to 8.

So instead of the quantity 3.05 times 7.95 minus 4 squared...

…we have the quantity 3 times 8 minus 4 squared, which is a lot simpler.

To get our answer, all we have to do is multiply everything out, following PEMDAS.

We do everything inside the square parentheses first,

and multiply 3 and 8 before subtracting 4.

3 times 8 is 24, and 24 minus 4 is 20.

Then we square that, giving us 20 squared equals 400.

The answer is B.