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3 years ago

What is the principal square root of -4

Mathematics

1 answer:

devlian [24]3 years ago

6 0

Answer:

The principal square root of -4 is 2i.

Step-by-step explanation:

$\sqrt{-4}$ = 2i

We have the following steps to get the answer:

Applying radical rule $\sqrt{-a} =\sqrt{-1} \sqrt{a}$

We get $\sqrt{-4} =\sqrt{-1} \sqrt{4}$

As per imaginary rule we know that $\sqrt{-1}=i$

= $\sqrt{4} i$

Now $\sqrt{4} =2$

Hence, the answer is 2i.

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ABC has the points A(1,7) B(-2,2) and C(4,2) as it’s vertices

tekilochka [14]

Part 1

Using the distance formula,

$AB=\sqrt{(-2-1)^{2}+(2-7)^{2}}=\sqrt{34}\\\\BC=\sqrt{(-2-4)^{2}+(2-2)^{2}}=6\\\\AC=\sqrt{(1-4)^{2}+(7-2)^{2}}=\sqrt{34}$

So, the measure of the longest side is 6 units.

Part 2

Triangle ABD will have vertices A(1,7), B(-2, 2), and D(1,2).

We already know that $AB=\sqrt{34}$

Using the distance formula,

$AD=\sqrt{(1-1)^{2}+(7-2)^{2}}=5\\\\BD=\sqrt{(-2-1)^{2}+(2-2)^{2}}=3$

So, ABD is a scalene triangle.

Part 3

From part 2, we know that the length of side AD is 5 units.

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2 years ago

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3 years ago

Which is NOT equivalent to 106? 10 × 10 × 10 × 10 × 10 × 10

lesya692 [45]

Answer: 10 × 6 is the answer 10 times 6= 60 not 106

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3 years ago

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Two sides of a triangle have the same length. The third side measures 7m less than twice the common length. The perimeter of the

Gwar [14]

Answer:

Step-by-step explanation:

I am pretty sure your answer is 3

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3 years ago

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PLEASE HELP Expand (r + 3)^2

vivado [14]

Answer:

r²+6r+9

Step-by-step explanation:

for the expansion of (r+3)², we use the formula as,

(a+b)²=a²+2ab+b²

here, we have

a=r

b=3

plug in all the values

(r+3)²=r²+2(r)(3)+3²

solving the equation

(r+3)²=r²+6r+9

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3 years ago