Perform the indicated division. Rationalize the denominator if necessary. Then simplify each radical expression.

Problem #54
(6-radical(20))/(2)

My answer: 3-radical(5)

Problem #50

Find the area of the rectangle shown in the figure.

width = radical (3) + radical (5)
Length = radical(3) + radical (5)

My answer: 15.75

first is correct. Second is correct.
As a side diversion, paste this into your Google search window.
(sqrt3 + sqrt5)^2

can you show me what you mean ...to paste ...thanks

Paste means copy.

oh okay thank you.....

To find the answer to Problem #54, we need to divide (6 - √20) by 2.

To do this, we can simplify the expression under the radical by factoring out any perfect squares. For √20, we can see that 4 is a perfect square, so we can rewrite it as √(4 * 5).

Using the property of radicals √(ab) = √a * √b, we can break down √(4 * 5) as (√4) * (√5), which simplifies to 2√5.

So now the expression becomes (6 - 2√5) / 2.

To divide a fraction by a whole number, we can simply divide the numerator by the denominator. So (6 - 2√5) / 2 becomes 6/2 - 2√5/2.

Simplifying further, we have 3 - √5.

Therefore, the simplified expression is 3 - √5.

For Problem #50, we need to find the area of the rectangle with the given width and length.

The width is given as √3 + √5, and the length is also √3 + √5.

To find the area of a rectangle, we multiply the width by the length.

Using the distributive property, we can multiply (√3 + √5) by (√3 + √5):

(√3 + √5) * (√3 + √5) = (√3 * √3) + (√3 * √5) + (√5 * √3) + (√5 * √5)

Simplifying further, we have 3 + √15 + √15 + 5.

Combining like terms, we have 8 + 2√15.

Therefore, the area of the rectangle is 8 + 2√15, or 15.75.

As for the side diversion, if you paste (sqrt3 + sqrt5)^2 into your Google search window, Google will calculate the result for you.

I hope this helps! Let me know if you have any more questions.