MATH 5:
February 3, 2013
ASSIGNMENT
Square roots
Square root of 𝑎 is a number whose square is equal to 𝑎. For example: square root
of 25 is 5, because 5! = 25.
Notation: square root of number 𝑎 is commonly denoted 𝑎.
Homework
For the homework, let me remind you that you should write solutions, showing
your calculations and your reasoning — not just answers! Do not write on this
homework assignment — use a separate sheet of paper instead; leave the
homework assignment in your folder for future reference.
1**. A street vendor sells two types of magazines, one for 25 cents and the other
for 40 cents. If she sold 100 magazines for $28.60, how many of them were 25cent magazines?
2**. Factor the following number into primes: 99! – 9! . [Hint: you do not have to
compute this number.]
3**. Replace stars by digits in the number 21*53* to make it divisible by 45 (hint:
remember divisibility test for division by 9?).
4**. A student noticed that if he takes a 2-digit number such as 82, writes the
digits in opposite order, and subtracts from the original number, then the result
will be divisible by 9: 82 − 28 = 54 = 9 × 6. Is it always so? Will it work for 3digit numbers as well?
5**. Find the following square roots. If you can not find the number exactly, at
least say between which two whole numbers the answer is, e.g., between 5 and 6.
(a)
(b)
(c)
(d)
(e)
16
81
10,000
10!
50
6**. Solve (different letters stand for different digits):
7***. A rectangular aquarium has base 100 cm by 40 cm and height of 50 cm. It
is filled with water to the depth of 48 cm. How much will the water level rise if
one places in the aquarium a rock of volume 10,000 𝑐𝑚! so that it is completely
submerged?
8*. Find square roots of the following numbers:
121, 625, 256, 225, 2025
9**. What do you think cubic root of a number would be? How can you find cubic
root of a number, for example fine cube root of 216, cube root of 512, cube root
cube root of 1728?