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.