Last month, when Joe took his puppy to the veterinarian, the puppy weighed 5.4 pounds. This month, the puppy weighed 7.56 pounds
1 answer:
<u>Answer:</u>
40%
<u>Step-by-step explanation:</u>
We are given that last month, Joe's puppy weight 5.4 pounds while this month, the puppy weighed 7.56 pounds.
We are to find the percentage increase of the weight of the puppy
We know that the formula of percentage increase if given by:
<em>Percentage increase = (new value - initial value)/initial value × 100</em>
So substituting the given values to get:
Percentage increase in puppy's weight = = 40%
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Answer: To know whether a radical expression is in simplest form or not you should put the numbers and letters inside the radical in terms of prime factors. Then, the radical expression is in the simplest form if all the numbers and letters inside the radical are prime factors with a power less than the index of the radical
Explanation:
Any prime factor raised to a power greater than the index of the root can be simplified and any factor raised to a power less than the index of the root cannot be simplified
For example simplify the following radical in its simplest form:
![\sqrt[5]{3645 a^8b^7c^3}](https://tex.z-dn.net/?f=%20%5Csqrt%5B5%5D%7B3645%20a%5E8b%5E7c%5E3%7D%20)
1) Factor 3645 in its prime factors: 3645 = 3^6 * 5
2) Since the powr of 3 is 6, and 6 can be divided by the index of the root, 5, you can simplify in this way:
- 6 ÷ 5 = 1 with reminder 1, so 3^1 leaves the radical and 3^1 stays in the radical
3) since the factor 5 has power 1 it can not leave the radical
4) the power of a is 8, then:
8 ÷ 5 = 1 with reminder 3 => a^1 leaves the radical and a^3 stays inside the radical.
5) the power of b is 7, then:
7 ÷ 5 = 1 with reminder 2 => b^1 leaves the radical and b^2 stays inside the radical
6) the power of c is 3. Since 3 is less than 5 (the index of the radical) c^3 stays inside the radical.
7) the expression simplified to its simplest form is
![3ab \sqrt[5]{3.5.a^3b^2c^3}](https://tex.z-dn.net/?f=3ab%20%5Csqrt%5B5%5D%7B3.5.a%5E3b%5E2c%5E3%7D%20)
And you know it cannot be further simplified because all the numbers and letters inside the radical are prime factors with a power less than the index of the radical.
Explanation:
Any prime factor raised to a power greater than the index of the root can be simplified and any factor raised to a power less than the index of the root cannot be simplified
For example simplify the following radical in its simplest form:
1) Factor 3645 in its prime factors: 3645 = 3^6 * 5
2) Since the powr of 3 is 6, and 6 can be divided by the index of the root, 5, you can simplify in this way:
- 6 ÷ 5 = 1 with reminder 1, so 3^1 leaves the radical and 3^1 stays in the radical
3) since the factor 5 has power 1 it can not leave the radical
4) the power of a is 8, then:
8 ÷ 5 = 1 with reminder 3 => a^1 leaves the radical and a^3 stays inside the radical.
5) the power of b is 7, then:
7 ÷ 5 = 1 with reminder 2 => b^1 leaves the radical and b^2 stays inside the radical
6) the power of c is 3. Since 3 is less than 5 (the index of the radical) c^3 stays inside the radical.
7) the expression simplified to its simplest form is
And you know it cannot be further simplified because all the numbers and letters inside the radical are prime factors with a power less than the index of the radical.