Write each expression in simplest form.
( means square root
4. 3�(11 + 4�(11 Answer: 8(11
7. 7�(2 - 2(8 Answer: 1(2 ??
8. �(48 + �(75 Answer: 9(3
9.(3(10) Answer: 19 + 6�ã10
10. �(27/64 (Fractions) Answer: 3(3/8 ??
11. 10(20 - 3(80 Answer: 10(5
12. �(6/49 (Fractions)
Answer: �(6/7 ??
13. 3(2 * �(14 Answer:stays the same ??
14. �( 6/5o Answer: 10(3
15. �(30 * 2(12 Answer: �(30 * 4(3�
If I got any of these wrong, can someone please tell me how to do them correctly?
To simplify the given expressions, let's go through each one step by step:
4. 3�(11 + 4�(11)
To simplify this expression, we can calculate the value inside the innermost parenthesis first.
11 + 4�(11) = 11 + 4 * √(11) = 11 + 4 * √(11)
Now, multiply 4 with the square root of 11.
= 11 + 4(√11)
Finally, multiply 3 with the result obtained above.
= 3 * [11 + 4(√11)]
= 3 * 11 + 3 * 4(√11)
= 33 + 12(√11)
= 33 + 12√11
So, the simplified expression is 33 + 12√11, which you have correctly represented as 8(11).
7. 7�(2 - 2(8)
To simplify this expression, again, perform calculations inside the innermost parenthesis first.
2 - 2(8)
= 2 - 2 * 8
= 2 - 16
= -14
Now multiply 7 with the result obtained above.
7 * (-14)
= -98
So, the simplified expression is -98, which differs from your answer of 1(2).
8. �(48 + �(75)
Starting again with the innermost parenthesis, we have:
√75 = √(25 * 3) = 5 * √3
Now, substitute the value of √75 into the outermost parenthesis:
√48 + 5 * √3
= 4√3 + 5√3
= 9√3
Therefore, the simplified expression is 9√3, which you correctly represented as 9(3).
9. (3(10)
To simplify this expression, multiply 3 with 10:
3 * 10
= 30
So, the simplified expression is 30, which differs from your answer of 19 + 6�ã10.
10. �(27/64 (Fractions)
To simplify this expression, we can first simplify the fraction inside the square root:
√(27/64) = √(27)/√(64) = 3/8
Thus, the simplified expression is 3/8, which differs from your answer of 3(3/8).
11. 10(20 - 3(80)
Calculating inside the innermost parenthesis first:
20 - 3(80)
= 20 - 3 * 80
= 20 - 240
= -220
Now multiplying 10 with the result obtained above:
10 * (-220)
= -2200
So, the simplified expression is -2200, which differs from your answer of 10(5).
12. �(6/49 (Fractions)
To simplify this expression, we can simplify the fraction inside the square root:
√(6/49) = √(6)/√(49) = √(6)/7
So, the simplified expression is √(6)/7 (or √(6)/7), which differs from your answer of √(6/7).
13. 3(2 * �(14)
This expression doesn't require simplification since there are no innermost parentheses.
The expression stays the same as 3(2 * √14) or 6√14.
14. �( 6/5)
To simplify this expression, we can't simplify the fraction 6/5 further, so the answer remains as √(6/5), or √(6/5).
15. �(30 * 2(12)
Firstly, calculate the result inside the innermost parentheses:
2(12) = 2 * 12 = 24
Now substitute the value of 24 into the outermost parenthesis:
√(30 * 24) = √720
The simplified form of the square root of 720 is √(16 * 45) = 4√45, which matches your answer of √(30 * 4(3)).
I hope this clears up any confusion and helps you understand how to simplify these expressions correctly.