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QuestionEvaluate the following radicals:
26. 16+33\sqrt{16+33}
27. 200−753\sqrt[3]{200-75}
28. −24(9)3\sqrt[3]{-24(9)}
29. 234332 \sqrt[3]{343}
30. 20+443−36\sqrt[3]{20+44}-\sqrt{36}
31. 400−2324\sqrt{400}-2 \sqrt{324}
32. 81−2−83\sqrt{81}-2 \sqrt[3]{-8}
33. 598÷2+4255 \sqrt{98 \div 2}+4 \sqrt{25}
34. 3(−273−1253)3(\sqrt[3]{-27}-\sqrt[3]{125})

Studdy Solution

STEP 1

Assumptions1. The radical expressions are given in the form an\sqrt[n]{a} or banb\sqrt[n]{a} or an−bn\sqrt[n]{a}-\sqrt[n]{b} or ban−cdnb\sqrt[n]{a}-c\sqrt[n]{d} or b(an−cn)b(\sqrt[n]{a}-\sqrt[n]{c}) where n is the root, a and b are the numbers under the root and b and c are the coefficients of the roots. . The operations inside the root are performed before taking the root.
3. The roots are real numbers.

STEP 2

Evaluate the expression 16+33\sqrt{16+33}.
First, perform the addition inside the square root.
16+33=49\sqrt{16+33} = \sqrt{49}

STEP 3

Calculate the square root of49.
49=7\sqrt{49} =7

STEP 4

Evaluate the expression 200−753\sqrt[3]{200-75}.
First, perform the subtraction inside the cube root.
200−753=1253\sqrt[3]{200-75} = \sqrt[3]{125}

STEP 5

Calculate the cube root of125.
1253=5\sqrt[3]{125} =5

STEP 6

Evaluate the expression −24(9)3\sqrt[3]{-24(9)}.
First, perform the multiplication inside the cube root.
−24(9)3=−2163\sqrt[3]{-24(9)} = \sqrt[3]{-216}

STEP 7

Calculate the cube root of -216.
−2163=−6\sqrt[3]{-216} = -6

STEP 8

Evaluate the expression 234332 \sqrt[3]{343}.
First, calculate the cube root of343.
23433=2⋅72 \sqrt[3]{343} =2 \cdot7

STEP 9

Perform the multiplication.
2⋅7=142 \cdot7 =14

STEP 10

Evaluate the expression 20+443−36\sqrt[3]{20+44}-\sqrt{36}.
First, perform the addition inside the cube root and calculate the square root of36.
20+443−36=643−6\sqrt[3]{20+44}-\sqrt{36} = \sqrt[3]{64}-6

STEP 11

Calculate the cube root of64 and perform the subtraction.
643−6=4−6=−\sqrt[3]{64}-6 =4-6 = -

STEP 12

Evaluate the expression 400−2324\sqrt{400}-2 \sqrt{324}.
First, calculate the square roots of400 and324.
400−2324=20−2⋅18\sqrt{400}-2 \sqrt{324} =20-2 \cdot18

STEP 13

Perform the multiplication and the subtraction.
20−2⋅18=20−36=−1620-2 \cdot18 =20-36 = -16

STEP 14

Evaluate the expression 81−2−83\sqrt{81}-2 \sqrt[3]{-8}.
First, calculate the square root of81 and the cube root of -8.
81−2−83=9−2⋅(−2)\sqrt{81}-2 \sqrt[3]{-8} =9-2 \cdot (-2)

STEP 15

Perform the multiplication and the subtraction.
9−2⋅(−2)=9+4=139-2 \cdot (-2) =9+4 =13

STEP 16

Evaluate the expression 598÷2+4255 \sqrt{98 \div2}+4 \sqrt{25}.
First, perform the division inside the square root and calculate the square root of25.
598÷2+425=549+4⋅55 \sqrt{98 \div2}+4 \sqrt{25} =5 \sqrt{49}+4 \cdot5

STEP 17

Calculate the square root of49, perform the multiplication and the addition.
549+4⋅5=5⋅7+20=35+20=555 \sqrt{49}+4 \cdot5 =5 \cdot7+20 =35+20 =55

STEP 18

Evaluate the expression 3(−273−1253)3(\sqrt[3]{-27}-\sqrt[3]{125}).
First, calculate the cube roots of -27 and125.
3(−273−1253)=3(−3−5)3(\sqrt[3]{-27}-\sqrt[3]{125}) =3(-3-5)

STEP 19

Perform the subtraction and the multiplication.
3(−3−5)=3⋅(−8)=−243(-3-5) =3 \cdot (-8) = -24The solutions are7,5, -6,14, -, -16,13,55, -24

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