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Zorluk: KolayExponents, Roots, and Scientific Notation

Evaluate the mathematical expressions below and arrange them in order from least to greatest value.

  1. 125\sqrt{25}
  2. 2232^3
  3. 31.2×1011.2 \times 10^1

Cevap

The correct order from least to greatest is 25\sqrt{25}, 232^3, and 1.2×1011.2 \times 10^1.
Evaluating each expression gives 25=5\sqrt{25} = 5, 23=82^3 = 8, and 1.2×101=121.2 \times 10^1 = 12. Comparing these values gives 5<8<125 < 8 < 12, which yields the sequence: 25\sqrt{25}, 232^3, and 1.2×1011.2 \times 10^1.

Adım Adım Çözüm

1
Evaluate the square root expression.
25=5\sqrt{25} = 5
Identify the non-negative number that, when multiplied by itself, equals 2525.
2
Evaluate the exponential expression.
23=82^3 = 8
Multiply the base, 22, by itself three times (2×2×22 \times 2 \times 2).
3
Evaluate the expression in scientific notation.
1.2×101=121.2 \times 10^1 = 12
Multiply 1.21.2 by 1010 to shift the decimal point one spot to the right.
4
Order the resulting values from least to greatest.
5<8<125 < 8 < 12, which corresponds to the expressions: 25\sqrt{25}, 232^3, and 1.2×1011.2 \times 10^1.
Compare the numbers 55, 88, and 1212 to establish their relative sizes.

Anahtar Kavram

Evaluating basic exponents, square roots, and scientific notation, then ordering their values.
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