14. (2 + √2)(2 – √2)
0
2
6 + 4√2
4 + √2
15. √15(√10 - 2)
5√6 - 2√15
√25 - 2√15
√150 - 2
√150 - 2√15
16. Find an exact solution for √5 - 1/x = √5/2. Then find the approximate solution to the nearest tenth.
10 - 2√5/5; 1.1
2 - 2√5; -2.5
–2; –2
2√5 - 5/√5; 1.1
17. 9 = √d + 2
3.5
√7
49
7
18. √a - 4 = 8
68
12
20
60
20. Find the domain of y = 3√3x - 3.
x > 1
x >/= -1
x >/= 1
x > -1
0
2
6 + 4√2
4 + √2
15. √15(√10 - 2)
5√6 - 2√15
√25 - 2√15
√150 - 2
√150 - 2√15
16. Find an exact solution for √5 - 1/x = √5/2. Then find the approximate solution to the nearest tenth.
10 - 2√5/5; 1.1
2 - 2√5; -2.5
–2; –2
2√5 - 5/√5; 1.1
17. 9 = √d + 2
3.5
√7
49
7
18. √a - 4 = 8
68
12
20
60
20. Find the domain of y = 3√3x - 3.
x > 1
x >/= -1
x >/= 1
x > -1
-
14. (2 + √2)(2 – √2)
Recall that (x + y) (x - y) = x² - y²
(2 + √2)(2 – √2) = 2² - √2² = 4 - 2 = 2
------------------------------
15.
√15(√10 - 2)
= √150 - 2√15
= √(25*6) - 2√15
= √25 √6 - 2√15
= 5√6 - 2√15
------------------------------
16.
√5 - 1/x = √5/2
√5 - √5/2 = 1/x
(2√5 - √5)/2 = 1/x
√5/2 = 1/x
x = 2/√5 = 0.9
This matches none of the answers shown, so I assume you must have forgotten brackets. Please be careful with this, since it can lead to erroneous results.
(√5 - 1)/x = √5/2
Cross multiply:
√5 x = 2√5 - 2
x = 2 - 2/√5
x = 2 - 2√5/5
x = (10 - 2√5)/5 = 1.1 (You forgot brackets in answers too!)
------------------------------
17.
9 = √d + 2
√d = 9 - 2
√d = 7
d = 7^2
d = 49
------------------------------
18.
√a - 4 = 8
√a = 8 + 4
√a = 12
a = 12^2
a = 144
Does not match any of the answers listed. Assume you forgot brackets again:
√(a - 4) = 8
a - 4 = 8^2
a - 4 = 64
a = 64 + 4
a = 68
------------------------------
20.
Looking at answers, I assume there must be brackets missing, so I'm jumping straight to that instead of attempting to solve as though there should be no brackets as indicated:
y = 3 √(3x - 3)
Valid only if argument under square root is non-negative
3x - 3 ≥ 0
3x ≥ 3
x ≥ 1
------------------------------
NOTE how important the use of brackets is. I'm not just saying this to be difficult, but it certainly helps those of us who are trying to help you get the correct answers to your questions.
Recall that (x + y) (x - y) = x² - y²
(2 + √2)(2 – √2) = 2² - √2² = 4 - 2 = 2
------------------------------
15.
√15(√10 - 2)
= √150 - 2√15
= √(25*6) - 2√15
= √25 √6 - 2√15
= 5√6 - 2√15
------------------------------
16.
√5 - 1/x = √5/2
√5 - √5/2 = 1/x
(2√5 - √5)/2 = 1/x
√5/2 = 1/x
x = 2/√5 = 0.9
This matches none of the answers shown, so I assume you must have forgotten brackets. Please be careful with this, since it can lead to erroneous results.
(√5 - 1)/x = √5/2
Cross multiply:
√5 x = 2√5 - 2
x = 2 - 2/√5
x = 2 - 2√5/5
x = (10 - 2√5)/5 = 1.1 (You forgot brackets in answers too!)
------------------------------
17.
9 = √d + 2
√d = 9 - 2
√d = 7
d = 7^2
d = 49
------------------------------
18.
√a - 4 = 8
√a = 8 + 4
√a = 12
a = 12^2
a = 144
Does not match any of the answers listed. Assume you forgot brackets again:
√(a - 4) = 8
a - 4 = 8^2
a - 4 = 64
a = 64 + 4
a = 68
------------------------------
20.
Looking at answers, I assume there must be brackets missing, so I'm jumping straight to that instead of attempting to solve as though there should be no brackets as indicated:
y = 3 √(3x - 3)
Valid only if argument under square root is non-negative
3x - 3 ≥ 0
3x ≥ 3
x ≥ 1
------------------------------
NOTE how important the use of brackets is. I'm not just saying this to be difficult, but it certainly helps those of us who are trying to help you get the correct answers to your questions.
-
(2 + √2)(2 – √2)
4 - 2√2 + 2√2 - 2
2
√15(√10 - 2)
√150 - 2√15
150 = 2 x 3 x 5 x 5 so simplify;
5√6 - 2√15
√5 - 1/x = √5/2
dunno
9 = √d + 2
√d = 9 - 2
d = 7²
d = 49
√a - 4 = 8
√a = 8 + 4
a = 12²
a = 144
y = 3√3x - 3
y = √27x - 3
√27x = y + 3
27x = (y+3)²
27x = y² + 6y + 9
x = (y² + 6y + 9) / 27
aaaaand .... I dunno
4 - 2√2 + 2√2 - 2
2
√15(√10 - 2)
√150 - 2√15
150 = 2 x 3 x 5 x 5 so simplify;
5√6 - 2√15
√5 - 1/x = √5/2
dunno
9 = √d + 2
√d = 9 - 2
d = 7²
d = 49
√a - 4 = 8
√a = 8 + 4
a = 12²
a = 144
y = 3√3x - 3
y = √27x - 3
√27x = y + 3
27x = (y+3)²
27x = y² + 6y + 9
x = (y² + 6y + 9) / 27
aaaaand .... I dunno