21. Find the square root ±√121
Is it 11?
28. Use the distributive property to simplify x(4x^2+x+4)
38. 4/5 + 2/10
Is it 3/5 ?
21. Find the square root ±√121
Is it 11?
yes, 11^2 = 121
28. Use the distributive property to simplify x(4x^2+x+4)
4 x^3 + 4 x^2 + 4 x
38. 4/5 + 2/10
Is it 3/5 ?
No 4/5 + 1/5 = 5/5 = 1
21. To find the square root of ±√121, we need to remember that the square root of a number is the value that, when multiplied by itself, gives the original number. In this case, ±√121 means both positive and negative square roots.
The square root of 121 is 11 (because 11 × 11 = 121). So, the positive square root is +11, and the negative square root is -11. Therefore, the answer is both +11 and -11.
28. To simplify x(4x^2+x+4) using the distributive property, we distribute x to each term inside the parentheses.
x(4x^2+x+4) = 4x^3 + x^2 + 4x
38. To find the sum of 4/5 + 2/10, we need to find a common denominator. The least common multiple of 5 and 10 is 10.
Next, we need to multiply the numerators and denominators by the appropriate factors to make the denominators equal to 10.
4/5 + 2/10 = (4 × 2)/(5 × 2) + (2 × 1)/(10 × 1) = 8/10 + 2/10
Now that the denominators are equal, you can simply add the numerators.
8/10 + 2/10 = (8 + 2)/10 = 10/10 = 1
Therefore, 4/5 + 2/10 simplifies to 1/1, which is equal to 1.
21. To find the square root of ±√121, you first need to determine the value of the square root. The square root of 121 is 11 because 11 multiplied by itself equals 121. However, the ± sign suggests that there might be two possible values for the square root: one positive and one negative. Therefore, the answer to ±√121 can be both +11 and -11.
28. To simplify the expression x(4x^2 + x + 4) using the distributive property, you need to multiply each term inside the parentheses by x. This means distributing x to every term.
Multiply x by 4x^2: x * 4x^2 = 4x^3
Multiply x by x: x * x = x^2
Multiply x by 4: x * 4 = 4x
Now, you can rewrite the simplified expression as: 4x^3 + x^2 + 4x.
38. To add fractions, such as 4/5 and 2/10, you need to find a common denominator. In this case, the least common denominator (LCD) is 10, as it is the smallest multiple of both 5 and 10.
To convert the fractions to have a denominator of 10, you need to multiply the numerator and denominator of 4/5 by 2 and the numerator and denominator of 2/10 by 5. This results in the following:
4/5 * 2/2 = 8/10
2/10 * 5/5 = 10/50
Now, you can add the fractions: 8/10 + 10/50. To add fractions with the same denominator, you simply add the numerators while keeping the denominator the same:
8/10 + 10/50 = 18/10.
However, this fraction can be simplified. Both the numerator and denominator can be divided by their greatest common divisor, which is 2. Dividing both 18 and 10 by 2 gives you:
18/10 = 9/5.
Therefore, the result of 4/5 + 2/10 is 9/5.