Test 2.1 Review Practice

Simplify √-54

Tags

CCSS.HSN.CN.A.1

CCSS.HSN.CN.A.2

CCSS.HSN.RN.A.2

CCSS.HSN.RN.A.1

Simplify i¹²⁰³

• 1

• i

• -1

• -i

Tags

CCSS.HSN.CN.A.1

Simplify √-75 + √-50

Tags

CCSS.HSN.CN.A.1

CCSS.HSN.CN.A.2

Rationalize: 4/(3i)

• 4/3

• 4i/3

• -4i/3

• -4/3

Answer explanation

multiply both top and bottom (of the fraction) by i, and use i^2 = -1 to simplify the denominator (bottom) to get the anwer

Tags

CCSS.HSA.APR.D.7

Simplify √-3√-12

• -6

• 6

• 6i

• -6i

Answer explanation

√-3 = i√3

√-12=i√12

the multiplication of the two factors equals i² √36, since i² = -1 and √36 = 6, we have

-6 as the answer

Tags

CCSS.HSN.CN.A.1

CCSS.HSN.CN.A.2

CCSS.HSN.RN.A.2

Simplify ( 6 ± √288) / 12

• 2 ± √2

• 1/2 ± i√2

• 2 ± i√2

• 1/2 ± √2

Answer explanation

√288 = √144*2 = 12√2

so (6±12√2)/12 = 6/12 ± 12√2/12

= 1/2 ± √2

Tags

CCSS.HSA-REI.B.4B

CCSS.HSN.CN.C.7

Simplify: (3 + 7i) (3 - 7i)

• 9 - 49 = - 40

• 9 + 49 = 58

• 9 + 42i - 40 = -31 + 42i

• 9 - 42i + 49 = 58 - 42i

Answer explanation

(3+7i) (3-7i) = 3² - (7i)² = 9 - 49i²

= 9+49 = 58

(because i² = -1)

(also because the FOIL, the OL two

terms +3*7i and -3*7i got cancelled:

i.e.: (3+7i) (3-7i) = 3² -3*7i + 3*7i - (7i)²

⁼ 3² - (7i)²

Tags

CCSS.HSA.APR.A.1

Rationalization: 5/ ( 2 + 3i)

Tags

CCSS.HSN.CN.A.3

Factor x² - 8x + 16

(a)  

Answer explanation

To factor x² - 8x + 16, we look for two identical numbers that multiply to 16 and add to -8. The numbers -4 and -4 fit this, so the expression factors to (x-4)(x-4), which is also written as (x-4)².

Tags

CCSS.HSA.APR.C.4

Factor the following expression: x² + 18x + 81

(a)  

Answer explanation

To factor x² + 18x + 81, we look for two numbers that multiply to 81 and add to 18. The numbers 9 and 9 fit this, so we can write the expression as (x+9)(x+9) or (x+9)².

Tags

CCSS.HSA.APR.C.4