If 68 is a prime number, then the only factors it has are 1 and 68.
If it has any other factors besides 1 and 68, then it's NOT prime.
Right away, without any higher math, you can look at just the last digit
in 68 . The last digit is '8'. That tells you that '68' is an even number,
and THAT tells you that '2' must be one of its factors. So '68' is not a
prime number.
The factors of 68 are 1, 2, 4, 17, 34, and 68 .
68 has four more factors besides 1 and 68, so it's not a prime number.
On a right triangle, to find one missing side you can use this equation
a^2 + b^2 = c^2
a and b are the sides next to the right angle, and c is the hypotenuse (side not connected to right angle).
You first need to find the length of the dotted line before finding x. This is because to be able to use the above formula, you have to know the length of two out of three of the sides.
To solve the length of the dotted line, note that it also makes a triangle with the 5 unit line and the 5 √5 unit line. You can plug these numbers into the formula.
(5)^2+b^2=(5 √5)^2
25+b^2=125
b^2=100
b=10
Now that you know the length of the dotted line is 10 units, you can now solve for x
(20)^2+(10)^2=x^2
400+100=x^2
500=x^2
x= √500, which equals 22.361
1. sqrt(98) = 7 sqrt(2)
2. sqrt(y^6) = y^3
3. sqrt(a^7) = a^7/2
4. sqrt(12x^3y^2) = 2xy sqrt(3x)
5. sqrt(36x^2y^4) = 6xy^2
6. sqrt(48ab^3) = 4b sqrt(3ab)
7. sqrt(10a^5b^2) = a^2b sqrt(10a)
8. sqrt(20x^3y^10 = 2xy^5 sqrt(5x)
