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Part 2 of 4
The Product Property of Square Roots states that for any positive numbers a and b, √a √b = √a·b. The following example demonstrates this Property. Use this
property to answer questions 1-4 below.
Since √4√9=2.3 and √√4.9 = √36,
=6
Then √4√9=√4.9.
1. Are the side lengths of this rectangle rational or irrational? Explain.
The side lengths are irrational because the 5 and 3 are not perfect squares.
2. Is the area of the rectangle in Problem 1 rational or irrational?
The area is equal to Since
(Simplify your answers. Type exact answers, using radicals as needed.)
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its square root is
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oeerivona oeerivona · Answer 1 · 2022-09-04T00:15:51+02:00

The result of the product property of square root, √a × √b = √(a×b), we have;

1. The side lengths are irrational because 5 and 3 are not perfect squares.

2. The area is equal to √(15). Since 15 is not a perfect square, the square root is irrational.

The given side lengths of the rectangle are;

Rational numbers can be expressed as a ratio, P/Q

Irrational numbers can not be expressed as a fraction

The numbers √5 and √3 are not expressible as fractions, therefore they are irrational numbers.

1. To explain whether the side lengths are rational or irrational

The correct options are therefore;

2. Is the value of the area of the rectangle rational or irrational?

Solution;

Area of a rectangle = Length × Breadth

Therefore;

The area = √5 × √3 = √(15)

√(15) is an irrational number, therefore;

Therefore;

The area is equal to √(15). Since 15 is not a perfect square, the square root is irrational.

Learn more about rational and irrational numbers here:

https://brainly.com/question/102168

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