For Question 1-8 Simplify the Radical Expression
*** - My Answer
1.√45
3√5***
2.√180x^2
6x√5***
3.√150x^3 k^4
5xk^2√6x***
4.√21y * 5√49y
35y√21***
5.(The square root sign applies for the whole equation; both numerator and denominator)
√64y^10 h^5 / 16y^12 h^3
2h / y***
6.√3 + 4√3
5√3***
7.2√6 + 3√96
14√6***
8.(5+√3)(5-√3)
22***
all correct. good job.
Yes
I'm sorry, I'm an AI language model and I'm not sure what you are referring to. Can you please provide more information or context so I can assist you better?
1. √45
- "Why did the math book go on a diet? Because it had too many square roots! Speaking of square roots, let's simplify this one. √45 can be written as √(9 * 5). And since √9 is 3, we are left with 3√5!"
2. √180x^2
- "Did you hear about the math teacher who got promoted? He finally found the root of his success! Let's find the root of this expression too. √180x^2 can be simplified to 6x√5. It looks like we've got the root of the problem!"
3. √150x^3 k^4
- "Why was the math book always tense? Because it had too many square roots to deal with! Let's relieve some tension by simplifying this expression. We can break down √150x^3 k^4 into 5xk^2√6x. Now we've achieved some square root relaxation!"
4. √21y * 5√49y
- "Why are square roots so good at playing poker? Because they always know when they're being squared! Speaking of squares, let's deal with this expression. √21y multiplied by 5√49y simplifies to 35y√21. Looks like our square roots are winning the poker game!"
5. √64y^10 h^5 / 16y^12 h^3
- "Why did the fraction go to therapy? Because it had numerator issues! Let's heal these issues by simplifying this radical expression. The square root of 64 is 8, and when we simplify the variables, we get 2h / y. It seems like our fraction is feeling much better now!"
6. √3 + 4√3
- "Why did the square root go to a party? Because it can't be negative! Let's add some square roots together. √3 plus 4√3 equals 5√3. It looks like they had a rootin' tootin' good time at the party!"
7. 2√6 + 3√96
- "Why did the math teacher use an umbrella? Because he had to solve some square roots! Let's solve them too. 2√6 plus 3√96 equals 14√6. Looks like our math teacher can dance in the rain now!"
8. (5 + √3)(5 - √3)
- "Why did the math equation go to the therapist? To solve its multi-parenthood issues! Let's simplify this expression. (5 + √3)(5 - √3) equals 22. Looks like our equation finally found some peace and closure!"
To simplify radical expressions, we follow these steps:
Step 1: Factorize all the numbers inside the root symbol into their prime factors.
Step 2: Group the factors in pairs, where each pair consists of the same number.
Step 3: Bring one factor of each pair out of the radical symbol and leave the other inside.
Step 4: Multiply the factors outside the radical symbol together.
Step 5: If there are any numbers left inside the radical symbol, leave them as they are.
Now, let's go through each question and explain how to simplify the given radical expressions.
1. √45
First, we factorize 45: 45 = 3 * 3 * 5.
Next, we group the factors in pairs: 45 = (3 * 3) * 5.
Then, we bring one factor of each pair out of the radical: 3 * √5.
Finally, we multiply the factors outside the radical: 3√5.
Therefore, the simplified radical expression is 3√5.
2. √180x^2
First, we factorize 180: 180 = 2 * 2 * 3 * 3 * 5.
Next, we group the factors in pairs: 180 = (2 * 2) * (3 * 3) * 5.
Then, we bring one factor of each pair out of the radical: 2 * 3 * √5.
Finally, we multiply the factors outside the radical: 6√5x^2.
Therefore, the simplified radical expression is 6√5x^2.
3. √150x^3 k^4
First, we factorize 150: 150 = 2 * 3 * 5 * 5.
Next, we group the factors in pairs: 150 = (2 * 5) * (3 * 5).
Then, we bring one factor of each pair out of the radical: 5 * √6x * k^2.
Finally, we multiply the factors outside the radical: 5xk^2√6x.
Therefore, the simplified radical expression is 5xk^2√6x.
4. √21y * 5√49y
First, we simplify each radical expression separately:
√21y = √(3 * 7 * y) = √3 * √7 * √y = √3 * √7y
5√49y = 5 * √(7 * 7 * y) = 5 * 7 * √y = 35√y
Multiplying both simplified expressions together: 35y√21.
Therefore, the simplified radical expression is 35y√21.
5. √64y^10 h^5 / 16y^12 h^3
We simplify each part of the expression and then divide them:
√64y^10 = √(2^6 * y^10) = 2^3 * y^5 = 8y^5
√16y^12 = √(2^4 * y^12) = 2^2 * y^6 = 4y^6
Dividing both expressions: (8y^5)/(4y^6) = 2/y.
Therefore, the simplified radical expression is 2/y.
6. √3 + 4√3
We can combine the two terms with the same radical:
√3 + 4√3 = 1√3 + 4√3 = (1 + 4)√3 = 5√3.
Therefore, the simplified radical expression is 5√3.
7. 2√6 + 3√96
First, we simplify each radical expression separately:
2√6 = 2 * √(2 * 3) = 2 * √6.
3√96 = 3 * √(2^5 * 3) = 3 * 2^2 * √6 = 12√6.
Adding both simplified expressions together: 2√6 + 12√6 = 14√6.
Therefore, the simplified radical expression is 14√6.
8. (5 + √3)(5 - √3)
Using the formula for the difference of squares, we have:
(5 + √3)(5 - √3) = 5^2 - (√3)^2 = 25 - 3 = 22.
Therefore, the simplified expression is 22.
In conclusion,
1. √45 simplifies to 3√5.
2. √180x^2 simplifies to 6x√5.
3. √150x^3 k^4 simplifies to 5xk^2√6x.
4. √21y * 5√49y simplifies to 35y√21.
5. √64y^10 h^5 / 16y^12 h^3 simplifies to 2/y.
6. √3 + 4√3 simplifies to 5√3.
7. 2√6 + 3√96 simplifies to 14√6.
8. (5 + √3)(5 - √3) simplifies to 22.