Question

7th grade, currently doing square roots.
The question was
What are the square roots of 400?
The answer was
The number 400 has a positive and a negative square root. Also, 400 = 20 to the second power.
So the square roots of 400 are 20 and -20.
Can someone explain how they came to that????

Answer 1

20 times 20 is 400

Answer 2

\[\sqrt{400}=\sqrt{x^{2}}\]
you can rewrite the number under the root sign
if you think of a square number that goes into 400, we will choose 4, and multiply it by a number to make 400
so 4 multiplied by 100
\[\sqrt{c}=\sqrt{a \times b}\]
\[\sqrt{400}=\sqrt{4 \times 100}\]

you can also seperate this by following the rule
\[\sqrt{a \times b}=\sqrt{a} \times \sqrt{b}\]
\[\sqrt{4 \times 100} = \sqrt{4} \times \sqrt{100}\]

\[\sqrt{4}=2\]
\[\sqrt{100}=10\]
2x10=20


and as you know, you always get a positive and negative answer


since
\[(-20) \times (-20)=(-1 \times -1)(20 \times 20)\]
negative multiplied by negative is a positive

or you can just remember the answer to the square of the first 20 numbers

Answer 3

I pretty much know the square root of 1-12 or so using 2..
Plus I really suck at Pre-Algebra
Thanks for the help!

Answer 4

to be honest you could just do trial and error, but you should memorise the squares of a number that is a multiple of 10

10x10=100
20x20=400
30x30=900

they are pretty easy since for 10
you square 1
then put as many zeros as you see
since 10x10 there are 2 zeros you get
100

for 20

2squared is 4
two zeros
400

so if you had to find the square root of 361

you know it is close to 20 squared since it is close to 400
and you know it is more than 10 squared
so try finding the square of a number half way between 10 and 20
15
15 squared is 225
it is between 15 and 20

try 17
17 squared is 289
between 17 and 20
try 19
19 squared is 361

more long winded

idk what way you prefer