South Dakota Grade 8 Math

Where is the square root of twenty-six?

Locate √26 between two consecutive hundredths. Start with 5² = 25 and 6² = 36, then compare the squares of rational decimal candidates. The symbol √26 denotes the nonnegative square root.

Follow the reasoning

Since 25 < 26 < 36, the positive root lies between 5 and 6. To narrow the interval, compute 5.09² = 25.9081 and 5.10² = 26.01. Squaring is increasing for nonnegative numbers, so 5.09 < √26 < 5.10. This brackets the root between consecutive hundredths without claiming either endpoint equals it. Refining further, 5.099² = 25.999801, so 5.099 is also a lower bound. A finite decimal displayed by a calculator is an approximation to √26, not an exact finite representation of this irrational number.

Separate a bound from an equality

Writing √26 = 5.10 incorrectly turns a rounded approximation into an exact equation. Use an approximation sign for a rounded value and inequalities for bounds. The positive-number condition matters when reasoning from squares; this argument does not claim that squaring preserves order for all negative numbers. Both −√26 and √26 solve x² = 26, but the radical symbol by itself names the nonnegative root.

Try the next step

Bracket √27 between consecutive hundredths by comparing 5.19² = 26.9361 with 5.20² = 27.04. Explain why 5.19 < √27 < 5.20, then mark a small interval on a clearly labeled number line. Compare the two root intervals without replacing either root with an exact finite decimal.

South Dakota mathematics references and edition transition

The South Dakota mathematics directory links both its 2018 and newly adopted 2026 editions. The assessed-standards timeline identifies 2026–27 as the mathematics transition year, 2027–28 for implementation, and 2028–29 for assessment of the new edition. This activity links the selected 2018 requirement for current teaching and identifies a related 2026 reference separately. Follow the school’s adopted materials and transition plan.

The 2018 document places numbered clauses beneath grade/domain headings; the reference above combines that heading and clause number. The 2026 edition reorganizes and renumbers requirements. These are selected related references, not a complete edition crosswalk, full curriculum, or certified alignment of every practice resource.

Choose a next task from the student’s explanation

Use a different set of numbers to check whether the student can explain the same relationship. If the explanation is unclear, return to the model; if the reasoning is sound but a calculation is wrong, work through a shorter calculation and check it against the model. Use the related learning resources alongside the teacher’s assigned goals.

The department’s current 2026–27 assessment table places the general English language arts and mathematics assessments in Grades 3–8, including Grade 8. Follow the school’s current directions and accommodations. Independently published practice has its own timing, tools, question count, and scoring; its result does not establish a state performance level. Read the current South Dakota assessment table.

State sources and the selected complete PDF page checked October 6, 2026. Confirm later guidance and local assignments before planning assessment preparation.