Jacob estimates the square root of 75 in the following way:

√75=3√25=3 * 5=15

(a) Explain why his reasoning is incorrect.
(b) Estimate the square root of 75 to the nearest thousandths without using your calculator. Show your work.

Note: If you use a calculator you will get the wrong answer.

a)

Step-by-step explanation:

Square root of 75 (√75) is regarded as a surd function because the value inside the square root sign is not a perfect square. In that case the given value will be splitted into the product of a largest perfect square and a prime number as shown:

√75 = √3×25

√75 = √3×√25

√75 = √3 × 5

√75 = 5√3

a) Based on the above calculation, it can be inferred that his reasoning is incorrect. The value of 3 was supposed to be inside a square root not a whole number i.e √3 × √25

b) Since √75 = 5√3

√75 = 5 × 1.7321

√75 = 8.6605

√75 = 8.661 {to nearest thousand}

$20.01

step-by-step explanation:

the sale price is (1.00 - 0.77)($87), or 0.23($87), or $20.01.