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Question

Please help me solve, but only what you can.

1. (√3+2√5)^2

2. √72b^7

3. 15-10√2-3√2+2√4

4. √96/4

5. (5√2+√3)(2√2-3√3)

Answer 1

1. (√3+2√5)^2 = 3+4√(15) +20 = 23 +4√(15)

2. √72b^7 =√(36*b^6)*√(2b) = 6b^3√(2b)

3. 15-10√2-3√2+2√4
=15 - 13√2 +2*2 = 19 -13√2

4. √96/4 = √24 = √4 * √6 = 2√6

5. (5√2+√3)(2√2-3√3)
=20 -15√6 + 2√6 - 9 = 11 -13√6

Answer 2

1. (√3+2√5)^2
= (3 + 4√15 + 20) = (23 + 4√15)

2. √72b^7
= 6b^3√2b

3. 15-10√2-3√2+2√4
= 19 - 13√2

4. √96/4
= √24 = 2√6

5. (5√2+√3)(2√2-3√3)
= (20 + 2√6 -15√6 -9) = 11 - 13√6

Answer 3

1. (√3+2√5)^2 = 3 + 4*5 + 4√15 = 23 + 4√15

2. √72b^7 = 373248b^3(√72b)

3. 15-10√2-3√2+2√4 = 15 - 9√2

4. √96/4 = 2√6

5. (5√2+√3)(2√2-3√3) = 10*2 -15√6 + 2√6 -9 = 11 - 13√6

Answer 4

1. 3 + 4rad15 + 20 = 23 + 4rad15

2. This is in reduced form.

3. 15 - 13rad2 + 2rad4 = 19 - 13rad2

4. rad16*rad6/4 = 4rad6/4 = rad6

5. 10*2 - 15rad6 + 2rad6 - 3*3 = 11 - 13rad6