316 MCGRAW-HILL’S SAT
Concept Review 4
- 4, 9, 16, 25, 36, 49, 64, 81, 100, 121
- They are “like” if their radicands (what’s inside
the radical) are the same. - An exponential is a perfect square only if its co-
efficient is a perfect squareand its exponent is even. - false:
- true:
- true:
- false if xis negative:
- 5 or − 5
- 64 or − 64
- (Law of Distribution)
11.
610
35
22
mn m
n= mm57 87 37−=−
81 xx^2 = 933393
(^542)
()xxxxx=()()=
32 58 32 102 132+=+ =
(^23) ()× xxx=×× =2 3 6
12.
13.
14.
15.
- can’t be simplified (unlike terms).
17.18.
19.
22 418
2
249 24321214
+
=+ =+×=+ =
12 12121222322
2
()+ =+()()+ =+ + = +()()3 5 7 2=21 10
63 +
552 54 13 1013=×=
54 3 49 3 103 123 23×− ×= − =−
512 4 27−=
23 243
3
()=()()gg^555 = g^2Answer Key 4: Working with Roots
SAT Practice 4
1.B The square root of^1 ⁄ 4 is^1 ⁄ 2 , because (^1 ⁄ 2 )^2 =^1 ⁄ 4.
Twice^1 ⁄ 4 is also^1 ⁄ 2 , because 2(^1 ⁄ 4 ) =^1 ⁄ 2. You can also set
it up algebraically:
Square both sides: x= 4 x^2
Divide by x(it’s okay; xis positive): 1 = 4 x
Divide by 4:^1 ⁄ 4 =x
- Any number between 1 and 4 (but not 1 or 4).
Guess and check is probably the most efficient
method here. Notice that only if x> 1, and
(^1) ⁄ 2 only if x< 4.
3.E a^2 =9, so a=3 or −3. b^2 =16, so b=4 or −4. The
greatest value of a−b,then, is 3 −(−4) =7.
4.A
Square both sides:
Multiply by y: 9 y^3 = 2
Divide by 9: y^3 =2/9
5.D If x^2 =4, then x=2 or −2, and if y^2 =9, then
y=3 or −3. But if (x−2)(y+3) ≠0, then xcannot
be 2 and ycannot be −3. Therefore, x=−2 and y=3.
(−2)^3 + 33 =− 8 + 27 = 19
9
2 2
y
y=
3
2
y
y=
xx<xx<xx= 26.D
Also, you can plug in easy positive values for m
and nlike 1 and 2, evaluate the expression on your
calculator, and check it against the choices.
7.C The diagonal is the hypotenuse of a right triangle,
so we can find its length with the Pythagorean
theorem:
Simplify: a+b=d^2
Take the square root:
Or you can plug in numbers for aand b,like 9 and
16, before you use the Pythagorean theorem.
8.C Assume that the squares have areas of 10 and- The lengths of their sides, then, are and 1,
respectively, and the perimeters are 4 and 4.
4 :4 = :1
9.B Use the Pythagorean theorem:Simplify: 1 +x^2 =n
Subtract 1: x^2 =n− 1
Take the square root:xn=− 1 (Or plug in!)122
2
+=xn()10 10
10
10
ab d+=()abd+()=(^222)
218
2
218
2
29 6
mn
mm
mn
= nn