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1 year ago

Can u guys pls help me with this homework

1 answer:

6 0

The value of √(7 * 23 - 1)/8 is 4.47, the values of a, b and c are -14/11, -10/11 and 3, respectively and the area of the shape is 5√5 + 5 square meters

<h3>How to evaluate the radical expression?</h3>

The question goes thus:

If √5 = 2.236, evaluate √(7 * 23 - 1)/8

We have:

√(7 * 23 - 1)/8

Evaluate the product of 7 and 23

√(7 * 23 - 1)/8 = √(161 - 1)/8

Evaluate the difference of 161 and 1

√(7 * 23 - 1)/8 = √160/8

Evaluate the quotient of 160 and 8

√(7 * 23 - 1)/8 = √20

Express 20 as the product 4 and 5

√(7 * 23 - 1)/8 = √(4 * 5)

Expand the product

√(7 * 23 - 1)/8 = √4 * √5

Express √4 as 2

√(7 * 23 - 1)/8 = 2 * √5

Substitute √5 = 2.236

√(7 * 23 - 1)/8 = 2 * 2.236

Evaluate the product

√(7 * 23 - 1)/8 = 4.472

Approximate

√(7 * 23 - 1)/8 = 4.47

Hence, the value of √(7 * 23 - 1)/8 is 4.47

<h3>How to simplify the radical expression?</h3>

The expression is given as:

(3√2 + 5√6)/(3√2 - 5√6)

Rationalize the above expression

(3√2 + 5√6)/(3√2 - 5√6) * (3√2 + 5√6)/(3√2 + 5√6)

Evaluate the product

(3√2 + 5√6)²/((3√2)² - (5√6)²)

Simplify the denominator

(3√2 + 5√6)²/(18 - 150)

This gives

[(3√2)² + (5√6)² + 2 *(3√2) * (5√6)]/(-132)

Simplify the numerator

[168 + 120√3]/(-132)

Simplify the fraction

-14/11 - 10√3/11

Hence, the values of a, b and c are -14/11, -10/11 and 3, respectively

<h3>How to determine the area?</h3>

The area is calculated as:

A = 1/2 * (Sum of parallel bases) * Height

So, we have:

A = 1/2 * (4 + 3√5 + 6 - √5) * √5

Evaluate the like terms

A = 1/2 * (10 + 2√5) * √5

Evaluate the product

A = (5 + √5) * √5

Evaluate the product

A = 5√5 + 5

Hence, the area of the shape is 5√5 + 5 square meters

Read more about rational expressions at:

brainly.com/question/8008240

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