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Selesaikan. Solve. (i) sqrt(13) x sqrt(13) (ii) 3/(216) + 43. (b) Diberi: Given: Cari nilai a + b. Find the value of a + b. -729 = a x a x a sqrt(49) = b + 2

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3 parts
a(ii)

641264\frac{1}{2}

b
-4

Step-by-step solution

9 steps

Here's the solution to question 3.

Part a(i)· 2 steps

Solve 13×13\sqrt{13} \times \sqrt{13}.

Selesaikan (Solve)

  1. Multiply the square roots.

    When a square root is multiplied by itself, the result is the number inside the square root.

    13×13=13×13=169\sqrt{13} \times \sqrt{13} = \sqrt{13 \times 13} = \sqrt{169}
  2. Simplify the square root.

    169=13\sqrt{169} = 13

    The solution is 13\boxed{13}.

Part a(ii)

641264\frac{1}{2}

Solve 272163+43\sqrt[3]{\frac{27}{216}} + 4^3.

  1. Evaluate the cube root of the fraction.

    Find the cube root of the numerator and the denominator separately.

    273=3(since 3×3×3=27)\sqrt[3]{27} = 3 \quad (\text{since } 3 \times 3 \times 3 = 27) 2163=6(since 6×6×6=216)\sqrt[3]{216} = 6 \quad (\text{since } 6 \times 6 \times 6 = 216)

    So,

    272163=2732163=36\sqrt[3]{\frac{27}{216}} = \frac{\sqrt[3]{27}}{\sqrt[3]{216}} = \frac{3}{6}
  2. Simplify the fraction.

    36=12\frac{3}{6} = \frac{1}{2}
  3. Evaluate 434^3.

    43=4×4×4=16×4=644^3 = 4 \times 4 \times 4 = 16 \times 4 = 64
  4. Add the results from Step 2 and Step 3.

    12+64=6412or64.5\frac{1}{2} + 64 = 64\frac{1}{2} \quad \text{or} \quad 64.5

    The solution is 6412\boxed{64\frac{1}{2}}.

Part b-4

Diberi (Given)

−729=a×a×a-729 = a \times a \times a
49=b+2\sqrt{49} = b + 2
Cari nilai a+ba+b. (Find the value of a+ba+b.)

  1. Find the value of aa.

    The equation is −729=a×a×a-729 = a \times a \times a, which can be written as a3=−729a^3 = -729.
    To find aa, take the cube root of −729-729.

    a=−7293a = \sqrt[3]{-729}

    Since 9×9×9=7299 \times 9 \times 9 = 729, then (−9)×(−9)×(−9)=−729(-9) \times (-9) \times (-9) = -729.
    So, a=−9a = -9.

  2. Find the value of bb.

    The equation is 49=b+2\sqrt{49} = b + 2.
    First, evaluate 49\sqrt{49}.

    49=7\sqrt{49} = 7

    Substitute this value into the equation:

    7=b+27 = b + 2

    Subtract 2 from both sides to solve for bb:

    b=7−2b = 7 - 2 b=5b = 5
  3. Find the value of a+ba+b.

    Substitute the values of aa and bb found in Step 1 and Step 2.

    a+b=−9+5a+b = -9 + 5 a+b=−4a+b = -4

    The value of a+ba+b is −4\boxed{-4}.

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