Simplify by combining like terms.

Problem #32

radical (63) - 2 radical (28) + 5 radical (7)

My answer: 4radical(7)

Problem #50
Find the perimeter of the triangle shown in the figure.

leg 1 = radical (5) - radical (3)
leg 2= radical (5) + radical (3)
Hypotenuse= 4

My answer: p = 4 + 2radical (5)

PROBLEM #4
Perform the indicated multiplication. Then simplify each radical expression.

radical (13) Times radical (5)

My answer: radical (65)

yes, yes, yes

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For Problem #32, to simplify by combining like terms, you need to combine the radicals with the same number inside them. In this case, you have radicals with 63, 28, and 7 inside them.

To combine them, you can add or subtract the coefficients of the radicals if they have the same number inside the radical.

radical (63) - 2 radical (28) + 5 radical (7)

The radical (63) cannot be simplified further because there are no perfect square factors of 63. However, radical (28) can be simplified as 2 radical (7), since the square root of 28 is equal to the square root of 4 times the square root of 7.

So now we have:

radical (63) - 2 radical (28) + 5 radical (7)

= radical (63) - 2 * 2 radical (7) + 5 radical (7)

= radical (63) - 4 radical (7) + 5 radical (7)

Now, we can simplify further by combining like terms:

= radical (63) + (5 - 4) radical (7)

= radical (63) + 1 radical (7)

= radical (63) + radical (7)

= radical (9 * 7) + radical (7)

= 3 radical (7) + radical (7)

= (3 + 1) radical (7)

= 4 radical (7)

So the simplified form of the expression is 4 radical (7).

For Problem #50, to find the perimeter of the triangle, you need to add the lengths of all three sides.

The lengths of the legs are given as radical (5) - radical (3) and radical (5) + radical (3), and the hypotenuse is given as 4.

Perimeter = leg 1 + leg 2 + hypotenuse

= (radical (5) - radical (3)) + (radical (5) + radical (3)) + 4

= radical (5) - radical (3) + radical (5) + radical (3) + 4

= (radical (5) + radical (5)) + (- radical (3) + radical (3)) + 4

= 2 radical (5) + 0 + 4

= 2 radical (5) + 4

So the perimeter of the triangle is p = 4 + 2 radical (5).

For Problem #4, to multiply two radicals, you can multiply the coefficients together and multiply the numbers inside the radicals together.

radical (13) times radical (5)

= radical (13 * 5)

= radical (65)

So the product of radical (13) and radical (5) is radical (65).